Chapter 8 Polygons and Area

Section 2 Angles in Polygons

The definitions for interior angles and exterior angles can be extended to include angles formed in any polygon. In the diagrams shown below, interior angles are red, and exterior angles are blue.

Shape Sides (n) n-2 180 * (n-2) Sum of Degrees of interior angles triangle quadrilateral pentagon nonagon

Example 1: Use the Polygon Interior Angles Theorem Find the sum of the measures of the interior angles of a convex heptagon.

Example 2: Find the Measure of an Interior Angle Find the measure of <A in the diagram.

Example 3: Interior Angles of a Regular Polygon Find the measure of an interior angle of a regular octagon.

Checkpoint: Find Measures of Interior Angles In 1-3, find the measure of <G.

Checkpoint: Find Measures of Interior Angles 4) Find the measure of an interior angle of a regular polygon with twelve sides.

Sum of Degrees of exterior angles Type equation here. Shape Sides (n) angles Sum of exterior angles Sum of Degrees of exterior angles triangle m∠1+m∠2+m∠3=360 quadrilateral m∠1+m∠2m+m∠3+m∠4=360 pentagon nonagon

Example 4: Find the Measure of an Exterior Angle Find the value of x. m∠1 + m∠2+m∠3+ x = 360 m∠1 = 95 m∠3 = 2x m∠2= 85 m∠4 = x 85+95+2x + x=360 180+2x=360 95+85+2x+x=360 180+3x=360 2x =360-180 3x=180 X= 180 X = 60

269 + =360 x=91 73+60+90+x+46=360 116+92+89+3X =360 297+3X=360 3X = 63 Checkpoint: Find Exterior Angle Measures Find the value of x. 116+92+89+3X =360 297+3X=360 3X = 63 X = 21 73+60+90+x+46=360 269 + =360 X • x=91

Checkpoint: Find Exterior Angle Measures Find the value of x.

EXIT SLIP