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.

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

TOO

A. 10

B. 12

C. 14

D. 15

A. Find the value of x in the diagram.

TOO

A. 72

B. 60

C. 45

D. 90

B. Find the measure of each exterior angle of a regular pentagon.

Homework• Pg. 398 # 13 – 37 odd, 49