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# Angle measures in polygons lesson

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### Angle measures in polygons lesson

1. 1. WARM UP PROBLEM In ABC, m A = x°, m B = 3x°, and m C = (4x – 12) ° . Find the measures of the three angles.ANSWER 24°, 72°, 84°
2. 2. If all the angles in a triangle add up to 180⁰…Then what about the angles in a QUADRILATERAL? Hey I see TWO triangles in there! 2 * 180 = 3600
3. 3. Or a PENTAGON? Hey I see THREE triangles in there!3 * 180 = 540o
4. 4. Or a HEXAGON? Hey I see FOUR triangles in there! 4 * 180 = 720o
5. 5. # of Sum of # of measures ofsides triangles interior angles3 1 1(180)=1804 2 2(180)=3605 3 3(180)=5406 4 4(180)=720n n-2 (n-2) • 180
6. 6. If a convex polygon has n sides, then the sum of the measure of the interior angles is (n – 2)(180 )
7. 7. If a regular convex polygonhas n sides, then the measureof one of the interior angles is ( n 2)180 n
8. 8. EX. 1 USE A REGULAR 15-GON TO ANSWER THEQUESTIONS. A)Find the sum of the measures of the interior angles. 2340 B) Find the measure of ONE interior angle 156
9. 9. Ex: 2 Find the value of x in the polygon x 126 100 143 130 117126 + 130 + 117 + 143 + 100 + x = 720 616 + x = 720 x = 104
10. 10. Ex: 3 The measure of each interior angle is 150°,how many sides does the regular polygon have?(n 2) 180 One interior angle n(n 2) 180 150 n(n 2)180 150n n 12 A regular180 n 360 150 n dodecagon 30n 360
11. 11. TWO MORE IMPORTANT TERMS
12. 12. The sum of the measures of the 1 exterior angles of a convex polygon, oneat each vertex, is 360 . 3 2m 1 m 2 m 3 360
13. 13. The sum of the measures of the 1 exterior angles of a 2 convex polygon, oneat each vertex, is 360 . 4 3m 1 m 2 m 3 m 4 360
14. 14. The sum of the 2 measures of the 1 exterior angles of a convex polygon, one 3at each vertex, is 360 . 5 4m 1 m 2 m 3 m 4 m 5 360
15. 15. The measure of each exteriorangle of a regular polygon is 360 n
16. 16. EX. 4 FIND THE MEASURE OF ONE EXTERIORANGLE OF A REGULAR 20-GON. sum of the exterior angles number of sides  360 20 18
17. 17. EX. 5 FIND THE MEASURE OF ONE EXTERIORANGLE OF A REGULAR HEPTAGON. sum of the exterior angles number of sides 360 7 51.4
18. 18. EX. 6 THE SUM OF THE MEASURES OF FIVEINTERIOR ANGLES OF A HEXAGON IS 625. WHATIS THE MEASURE OF THE SIXTH ANGLE? 95