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Transcript 
Warm ups
Find the range for the measure of the third side of
a triangle given that the measures of two sides
are 43 and 29.
Find n and list the sides of ΔPQR in order from
shortest to longest if m<P = 12n – 15,
m<Q = 7n + 26, and m<R = 8n – 47.
State the assumption you would make to start an
indirect proof of the statement.
If –2x ≥ 18, then x ≤ –9.
6-1 ANGLES OF
POLYGONS
Objective: Find and use the sum of the
measures of the interior and exterior angles
of a polygon.
Polygon Interior Angles Sum
Example 1
Find the sum of the measures of the interior
angles of a convex nonagon.
(n – 2) ● 180 = (9 – 2) ● 180
= 7 ● 180 or 1260
n=9
Simplify.
Answer: The sum of the measures is 1260.
Find the Interior Angles Sum of a Polygon
Example 2
Find the measure of each interior angle of
parallelogram RSTU.
Step 1: Find x using interior
Step 2: Plug the value of x into each angle.
Find the Interior Angles Sum of a Polygon
Try with a Partner
Find the sum of the measures of the interior
angles of a convex octagon.
A. 900
B. 1080
C. 1260
D. 1440
Try with a Partner
Find the value of x.
A. x = 7.8
B. x = 22.2
C. x = 15
D. x = 10
Example 3
The measure of an interior angle of a regular
polygon is 144. Find the number of sides in the
polygon.
A. 12
B. 9
C. 11
D. 10
Polygon Exterior Angles Sum
Example 4
Find the measure of each exterior angle of a
regular decagon.
Answer:
The measure of each exterior angle of a
regular decagon is 36.
Find Exterior Angle Measures of a Polygon
Example 5
Find the value of x in the diagram.
Find Exterior Angle Measures of a Polygon
Example 4 Answer
Use the Polygon Exterior Angles Sum Theorem to
write an equation. Then solve for x.
5x + (4x – 6) + (5x – 5) + (4x + 3) + (6x – 12) + (2x + 3) +
(5x + 5) = 360
(5x + 4x + 5x + 4x + 6x + 2x + 5x) + [(–6) + (–5) + 3 +
(–12) + 3 + 5] = 360
31x – 12 = 360
31x = 372
x = 12
Answer:
x = 12
Find Exterior Angle Measures of a Polygon
TOO
A. Find the value of x in
the diagram.
A. 10
B. 12
C. 14
D. 15
TOO
B. Find the measure of each exterior angle of a
regular pentagon.
A. 72
B. 60
C. 45
D. 90
Homework
• Pg. 398 # 13 – 37 odd, 49
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