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Warm ups
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.
Find the range for the measure of the third side of a triangle given that the measures of two sides are 43 and 29.
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6-1 ANGLES OF POLYGONSObjective: Find and use the sum of the measures of the interior and exterior angles of a polygon.
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Polygon Interior Angles Sum
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Example 1
Find the Interior Angles Sum of a Polygon
Find the sum of the measures of the interior angles of a convex nonagon.
(n – 2) ● 180 = (9 – 2) ● 180 n = 9
= 7 ● 180 or 1260 Simplify.
Answer: The sum of the measures is 1260.
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Example 2
Find the Interior Angles Sum of a Polygon
Find the measure of each interior angle of parallelogram RSTU.
Step 1: Find x using interiorStep 2: Plug the value of x into each angle.
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Try with a Partner
A. 900
B. 1080
C. 1260
D. 1440
Find the sum of the measures of the interior angles of a convex octagon.
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Try with a Partner
A. x = 7.8
B. x = 22.2
C. x = 15
D. x = 10
Find the value of x.
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Example 3
A. 12
B. 9
C. 11
D. 10
The measure of an interior angle of a regular polygon is 144. Find the number of sides in the polygon.
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Polygon Exterior Angles Sum
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Example 4
Find Exterior Angle Measures of a Polygon
Find the measure of each exterior angle of a regular decagon.
Answer: The measure of each exterior angle of aregular decagon is 36.
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Example 5
Find Exterior Angle Measures of a Polygon
Find the value of x in the diagram.
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Example 4 Answer
Find Exterior Angle Measures of a Polygon
Use the Polygon Exterior Angles Sum Theorem to write an equation. Then solve for x.
Answer: x = 12
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
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TOO
A. 10
B. 12
C. 14
D. 15
A. Find the value of x in the diagram.
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TOO
A. 72
B. 60
C. 45
D. 90
B. Find the measure of each exterior angle of a regular pentagon.
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Homework• Pg. 398 # 13 – 37 odd, 49