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°

3. 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

4. Or a PENTAGON?
Hey I see
THREE
triangles in
there!
3 * 180 = 540o

5. Or a HEXAGON?
Hey I see
FOUR
triangles in
there!
4 * 180 = 720o

6. # of Sum of
# of measures of
sides triangles interior angles
3 1 1(180)=180
4 2 2(180)=360
5 3 3(180)=540
6 4 4(180)=720
n n-2 (n-2) • 180

7. If a convex polygon has n sides,
then the sum of the measure of
the interior angles is
(n – 2)(180 )

8. If a regular convex polygon
has n sides, then the measure
of one of the interior angles is
( n 2)180
n

9. EX. 1 USE A REGULAR 15-GON TO ANSWER THE
QUESTIONS.
A)Find the sum of the measures of the
interior angles. 2340
B) Find the measure of ONE interior angle
156

10. Ex: 2 Find the value of x in the polygon
x
126 100
143
130 117
126 + 130 + 117 + 143 + 100 + x = 720
616 + x = 720
x = 104

11. 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 regular
180 n 360 150 n dodecagon
30n 360

12. TWO MORE IMPORTANT TERMS

13. The sum of the
measures of the 1
exterior angles of a
convex polygon, one
at each vertex, is 360 .
3
2
m 1 m 2 m 3 360

14. The sum of the
measures of the 1
exterior angles of a 2
convex polygon, one
at each vertex, is 360 .
4
3
m 1 m 2 m 3 m 4 360

15. The sum of the
2
measures of the
1
exterior angles of a
convex polygon, one 3
at each vertex, is 360 .
5
4
m 1 m 2 m 3 m 4 m 5 360

16. The measure of each exterior
angle of a regular polygon is
360
n

17. EX. 4 FIND THE MEASURE OF ONE EXTERIOR
ANGLE OF A REGULAR 20-GON.
sum of the exterior angles
number of sides

360
20
18

18. EX. 5 FIND THE MEASURE OF ONE EXTERIOR
ANGLE OF A REGULAR HEPTAGON.
sum of the exterior angles
number of sides
360
7
51.4

19. EX. 6 THE SUM OF THE MEASURES OF FIVE
INTERIOR ANGLES OF A HEXAGON IS 625. WHAT
IS THE MEASURE OF THE SIXTH ANGLE?
95