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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Warm ups Find n and list the sides of ΔPQR in order from shortest to longest if m Publish Lewis McDonald, Modified 5 months ago
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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.
6-1 ANGLES OF POLYGONSObjective: 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 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.
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.
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.
Try with a Partner
A. x = 7.8
B. x = 22.2
C. x = 15
D. x = 10
Find the value of x.
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.
Polygon Exterior Angles Sum
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.
Example 5
Find Exterior Angle Measures of a Polygon
Find the value of x in the diagram.
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.