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.

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Presentation transcript:

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 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 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) ● 180n = 9 =7 ● 180 or 1260Simplify. 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 interior Step 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 a regular 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) (–12) ]=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