1.
Section 5-7 Diagonals and Angles of PolygonsWed, Feb 02
2.
Essential Questions ✤ How are polygons classiﬁed according to their sides? ✤ How do you ﬁnd the sum of the angle measures of polygons? ✤ Where you’ll see this: ✤ Safety, hobbies, natureWed, Feb 02
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Vocabulary 1. Polygon: A closed ﬁgure made by joining three or more segments at their endpoints 2. Side: 3. Vertex: 4. Convex: 5. Concave: 6. Regular Polygon: 7. Diagonal:Wed, Feb 02
5.
Vocabulary 1. Polygon: A closed ﬁgure made by joining three or more segments at their endpoints 2. Side: One of the segments that makes up the polygon 3. Vertex: 4. Convex: 5. Concave: 6. Regular Polygon: 7. Diagonal:Wed, Feb 02
6.
Vocabulary 1. Polygon: A closed ﬁgure made by joining three or more segments at their endpoints 2. Side: One of the segments that makes up the polygon 3. Vertex: The point where segments meet 4. Convex: 5. Concave: 6. Regular Polygon: 7. Diagonal:Wed, Feb 02
7.
Vocabulary 1. Polygon: A closed ﬁgure made by joining three or more segments at their endpoints 2. Side: One of the segments that makes up the polygon 3. Vertex: The point where segments meet 4. Convex: When there are no indentations in a polygon 5. Concave: 6. Regular Polygon: 7. Diagonal:Wed, Feb 02
8.
Vocabulary 1. Polygon: A closed ﬁgure made by joining three or more segments at their endpoints 2. Side: One of the segments that makes up the polygon 3. Vertex: The point where segments meet 4. Convex: When there are no indentations in a polygon 5. Concave: When there is an indentation into a polygon 6. Regular Polygon: 7. Diagonal:Wed, Feb 02
9.
Vocabulary 1. Polygon: A closed ﬁgure made by joining three or more segments at their endpoints 2. Side: One of the segments that makes up the polygon 3. Vertex: The point where segments meet 4. Convex: When there are no indentations in a polygon 5. Concave: When there is an indentation into a polygon 6. Regular Polygon: A polygon where all the sides and angles are congruent 7. Diagonal:Wed, Feb 02
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Vocabulary 1. Polygon: A closed ﬁgure made by joining three or more segments at their endpoints 2. Side: One of the segments that makes up the polygon 3. Vertex: The point where segments meet 4. Convex: When there are no indentations in a polygon 5. Concave: When there is an indentation into a polygon 6. Regular Polygon: A polygon where all the sides and angles are congruent 7. Diagonal: A segment that joins two vertices but is not a sideWed, Feb 02
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Polygons and Their Sides 5 sides: 6 sides: 7 sides: 8 sides: 9 sides: 10 sides:Wed, Feb 02
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Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon 8 sides: 9 sides: 10 sides:Wed, Feb 02
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Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon 8 sides: 9 sides: 10 sides:Wed, Feb 02
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Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon 8 sides: 9 sides: 10 sides:Wed, Feb 02
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Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon 8 sides: 9 sides: 10 sides:Wed, Feb 02
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Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides:Wed, Feb 02
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Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides:Wed, Feb 02
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Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: OctagonWed, Feb 02
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Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: OctagonWed, Feb 02
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Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: Octagon NonagonWed, Feb 02
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Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: Octagon NonagonWed, Feb 02
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Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: Octagon Nonagon DecagonWed, Feb 02
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Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: Octagon Nonagon DecagonWed, Feb 02
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Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: Octagon Nonagon Decagon Anything larger:Wed, Feb 02
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Polygons and Their Sides 5 sides: 6 sides: 7 sides: Pentagon Hexagon Heptagon 8 sides: 9 sides: 10 sides: Octagon Nonagon Decagon Anything larger: n-gon, where n is the number of sidesWed, Feb 02
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Example 1 Name each polygon by its number of sides and label as concave or convex.Wed, Feb 02
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Example 1 Name each polygon by its number of sides and label as concave or convex.Wed, Feb 02
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Example 1 Name each polygon by its number of sides and label as concave or convex. ConcaveWed, Feb 02
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Example 1 Name each polygon by its number of sides and label as concave or convex. Concave PentagonWed, Feb 02
30.
Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Convex PentagonWed, Feb 02
31.
Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Convex Pentagon OctagonWed, Feb 02
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Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Convex Pentagon Octagon ConvexWed, Feb 02
33.
Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Convex Pentagon Octagon Convex QuadrilateralWed, Feb 02
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Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Convex Pentagon Octagon Convex Concave QuadrilateralWed, Feb 02
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Example 1 Name each polygon by its number of sides and label as concave or convex. Concave Convex Pentagon Octagon Convex Concave Quadrilateral NonagonWed, Feb 02
36.
# of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
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# of sides: 3 # of sides: # of triangles: # of triangles: Degrees: Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
38.
# of sides: 3 # of sides: # of triangles: 1 # of triangles: Degrees: Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
39.
# of sides: 3 # of sides: # of triangles: 1 # of triangles: Degrees: 180° Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
40.
# of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: Degrees: 180° Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
41.
# of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: Degrees: 180° Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
42.
# of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
43.
# of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
44.
# of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
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# of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
46.
# of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: # of triangles: # of triangles: Degrees: Degrees:Wed, Feb 02
47.
# of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: # of triangles: 3 # of triangles: Degrees: Degrees:Wed, Feb 02
48.
# of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: # of triangles: 3 # of triangles: Degrees: 540° Degrees:Wed, Feb 02
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# of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: 6 # of triangles: 3 # of triangles: Degrees: 540° Degrees:Wed, Feb 02
50.
# of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: 6 # of triangles: 3 # of triangles: Degrees: 540° Degrees:Wed, Feb 02
51.
# of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: 6 # of triangles: 3 # of triangles: Degrees: 540° Degrees:Wed, Feb 02
52.
# of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: 6 # of triangles: 3 # of triangles: Degrees: 540° Degrees:Wed, Feb 02
53.
# of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: 6 # of triangles: 3 # of triangles: 4 Degrees: 540° Degrees:Wed, Feb 02
54.
# of sides: 3 # of sides: 4 # of triangles: 1 # of triangles: 2 Degrees: 180° Degrees: 360° # of sides: 5 # of sides: 6 # of triangles: 3 # of triangles: 4 Degrees: 540° Degrees: 720°Wed, Feb 02
55.
Angle Sum of a Polygon: Angle Measure of a Regular Polygon:Wed, Feb 02
56.
Angle Sum of a Polygon: The sum of the interior angles of a polygon with n sides is given by the formula Angle Measure of a Regular Polygon:Wed, Feb 02
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Angle Sum of a Polygon: The sum of the interior angles of a polygon with n sides is given by the formula Angle Measure of a Regular Polygon: The measure of each interior angle of a regular polygon with n sides is given by the formula (n − 2)180° S= nWed, Feb 02
58.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle.Wed, Feb 02
59.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A F B E C DWed, Feb 02
60.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x F B 10x E C DWed, Feb 02
61.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x F B 10x 3x + 8 E C 3x + 8 DWed, Feb 02
62.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x F B 10x 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
63.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x F B 8x - 12 10x 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
64.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x S = (n − 2)180° F B 8x - 12 10x 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
65.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x S = (n − 2)180° F B 8x - 12 10x S = (6 − 2)180° 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
66.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x S = (n − 2)180° F B 8x - 12 10x S = (6 − 2)180° S = (4)180° 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
67.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x S = (n − 2)180° F B 8x - 12 10x S = (6 − 2)180° S = (4)180° 7x - 22 3x + 8 S = 720° E C 3x + 8 DWed, Feb 02
68.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x S = (n − 2)180° F B 8x - 12 10x S = (6 − 2)180° S = (4)180° 7x - 22 3x + 8 S = 720° E C 3x + 8 The sum of all of the angles is 720° DWed, Feb 02
69.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x F B 8x - 12 10x 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
70.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x 2(10x) + 2(3x + 8) + 7x − 22 + 8x − 12 = 720° F B 8x - 12 10x 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
71.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x 2(10x) + 2(3x + 8) + 7x − 22 + 8x − 12 = 720° 20x + 6x + 16 + 7x − 22 + 8x − 12 = 720° F B 8x - 12 10x 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
72.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x 2(10x) + 2(3x + 8) + 7x − 22 + 8x − 12 = 720° 20x + 6x + 16 + 7x − 22 + 8x − 12 = 720° F B 8x - 12 10x 41x − 18 = 720° 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
73.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x 2(10x) + 2(3x + 8) + 7x − 22 + 8x − 12 = 720° 20x + 6x + 16 + 7x − 22 + 8x − 12 = 720° F B 8x - 12 10x 41x − 18 = 720° +18 +18 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
74.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x 2(10x) + 2(3x + 8) + 7x − 22 + 8x − 12 = 720° 20x + 6x + 16 + 7x − 22 + 8x − 12 = 720° F B 8x - 12 10x 41x − 18 = 720° +18 +18 41x = 738 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
75.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x 2(10x) + 2(3x + 8) + 7x − 22 + 8x − 12 = 720° 20x + 6x + 16 + 7x − 22 + 8x − 12 = 720° F B 8x - 12 10x 41x − 18 = 720° +18 +18 41x = 738 41 41 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
76.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x 2(10x) + 2(3x + 8) + 7x − 22 + 8x − 12 = 720° 20x + 6x + 16 + 7x − 22 + 8x − 12 = 720° F B 8x - 12 10x 41x − 18 = 720° +18 +18 41x = 738 41 41 7x - 22 3x + 8 E C x = 18 3x + 8 DWed, Feb 02
77.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x x = 18 F B 8x - 12 10x 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
78.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
79.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
80.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
81.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 3(18) + 8 = 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
82.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 3(18) + 8 = 62° 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
83.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 3(18) + 8 = 62° = m∠C = m∠D 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
84.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 3(18) + 8 = 62° = m∠C = m∠D 7(18) - 22 = 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
85.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 3(18) + 8 = 62° = m∠C = m∠D 7(18) - 22 = 104° 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
86.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 3(18) + 8 = 62° = m∠C = m∠D 7(18) - 22 = 104° = m∠E 7x - 22 3x + 8 E C 3x + 8 DWed, Feb 02
87.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 3(18) + 8 = 62° = m∠C = m∠D 7(18) - 22 = 104° = m∠E 7x - 22 3x + 8 E C 8(18) - 12 = 3x + 8 DWed, Feb 02
88.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 3(18) + 8 = 62° = m∠C = m∠D 7(18) - 22 = 104° = m∠E 7x - 22 3x + 8 E C 8(18) - 12 = 132° 3x + 8 DWed, Feb 02
89.
Example 2 In hexagon ABCDEF, m∠A = m∠B = 10x, m∠C = m∠D = 3x + 8, m∠E = 7x - 22, and m∠F = 8x - 12. Find the sum of the measures of the angles of the hexagon, then ﬁnd the measure of each angle. A 10x x = 18 F B 8x - 12 10x 10(18) = 180° = m∠A = m∠B 3(18) + 8 = 62° = m∠C = m∠D 7(18) - 22 = 104° = m∠E 7x - 22 3x + 8 E C 8(18) - 12 = 132° = m∠F 3x + 8 DWed, Feb 02
90.
Example 3 Find the measure of each angle of a regular 14-gon.Wed, Feb 02
91.
Example 3 Find the measure of each angle of a regular 14-gon. (n − 2)180° S= nWed, Feb 02
92.
Example 3 Find the measure of each angle of a regular 14-gon. (n − 2)180° S= n (14 − 2)180° S= 14Wed, Feb 02
93.
Example 3 Find the measure of each angle of a regular 14-gon. (n − 2)180° S= n (14 − 2)180° S= 14 (12)180° S= 14Wed, Feb 02
94.
Example 3 Find the measure of each angle of a regular 14-gon. (n − 2)180° S= n (14 − 2)180° S= 14 (12)180° S= 14 2160° S= 14Wed, Feb 02
95.
Example 3 Find the measure of each angle of a regular 14-gon. (n − 2)180° S= n (14 − 2)180° S= 14 S = 154 2 7 ° (12)180° S= 14 2160° S= 14Wed, Feb 02
97.
Problem Set p. 224 #1-33 odd “Liberty without learning is always in peril; learning without liberty is always in vain.” - John F. KennedyWed, Feb 02
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