WARM UP PROBLEM   In    ABC, m      A = x°, m   B = 3x°, and   m     C = (4x – 12) ° .   Find the measures of the three an...
If all the angles in a triangle add up to 180⁰…Then what about the angles in a QUADRILATERAL?                             ...
Or a PENTAGON?                        Hey I see                         THREE                       triangles in          ...
Or a HEXAGON?                      Hey I see                        FOUR                     triangles in                 ...
# of         Sum of # of                measures ofsides   triangles   interior angles3          1          1(180)=1804   ...
If a convex polygon has n sides, then the sum of the measure of       the interior angles is      (n – 2)(180 )
If a regular convex polygonhas n sides, then the measureof one of the interior angles is       ( n 2)180           n
EX. 1 USE A REGULAR 15-GON TO ANSWER THEQUESTIONS. A)Find the sum of the measures of the   interior angles. 2340 B) Find t...
Ex: 2 Find the value of x in the polygon                   x         126                    100                           ...
Ex: 3 The measure of each interior angle is 150°,how many sides does the regular polygon have?(n 2) 180              One i...
TWO MORE IMPORTANT TERMS
The sum of the    measures of the            1  exterior angles of a convex polygon, oneat each vertex, is 360 .          ...
The sum of the    measures of the        1  exterior angles of a               2 convex polygon, oneat each vertex, is 360...
The sum of the                               2    measures of the                           1  exterior angles of a convex...
The measure of each exteriorangle of a regular polygon is          360            n
EX. 4 FIND THE MEASURE OF ONE EXTERIORANGLE OF A REGULAR 20-GON.                     sum of the exterior angles           ...
EX. 5 FIND THE MEASURE OF ONE EXTERIORANGLE OF A REGULAR HEPTAGON. sum of the exterior angles     number of sides         ...
EX. 6 THE SUM OF THE MEASURES OF FIVEINTERIOR ANGLES OF A HEXAGON IS 625. WHATIS THE MEASURE OF THE SIXTH ANGLE?          ...
Angle measures in polygons lesson
Upcoming SlideShare
Loading in...5
×

Angle measures in polygons lesson

1,571

Published on

Published in: Technology, Education
0 Comments
1 Like
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total Views
1,571
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
37
Comments
0
Likes
1
Embeds 0
No embeds

No notes for slide

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
  1. A particular slide catching your eye?

    Clipping is a handy way to collect important slides you want to go back to later.

×