Lesson Menu Main Idea and New Vocabulary NGSSS Example 1:Classify Polygons Key Concept:Interior Angle Sum of a Polygon Example 2:Sum of Interior Angle Measures Example 3:Real-World Example Five-Minute Check

Main Idea/Vocabulary Find the sum of the angle measures of a polygon and the measure of an interior angle of a regular polygon. polygon interior angle equiangular regular polygon

NGSSS MA.8.G.2.3 Demonstrate that the sum of the angles in a triangle is 180-degrees and apply this fact to find unknown measure of angles, and the sum of angles in polygons.

Example 1 Classify Polygons Determine whether the figure is a polygon. If it is, classify the polygon. If it is not a polygon, explain why. Answer: It is not a polygon because it has a curved side.

Example 1 CYP A.yes; pentagon B.yes; hexagon C.yes; heptagon D.No; the segments do not intersect at their endpoints. Determine whether the figure is a polygon. If it is, classify the polygon. If it is not a polygon, explain why.

Key Concept 3

Example 2 ALGEBRA Find the sum of the measures of the interior angles of a 13-gon. Sum of Interior Angle Measures S = (n – 2)180 Write an equation. S = (13 – 2)180 A 13-gon has 13 sides. Replace n with 13. S = (11)180 or 1,980 Simplify. Answer:The sum of the measures of the interior angles of a 13-gon is 1,980°.

Example 2 CYP A.160° B.2,880° C.3,060° D.3,240° ALGEBRA Find the sum of the measures of the interior angles of an 18-gon.

Example 3 DESIGN A designer is creating a new logo for a bank. The logo consists of a regular pentagon surrounded by isosceles triangles. Find the measure of an interior angle of a regular pentagon.

Example 3 Step 1 Find the sum of the measures of the angles. S = (n – 2)180Write an equation. S = (5 – 2)180Replace n with 6. S = (3)180 or 540Simplify. The sum of the measures of the interior angles is 540°.

Example 3 Answer:The measure of one interior angle of a regular pentagon is 108°. Step 2 Divide 540 by 5, the number of interior angles, to find the measure of one interior angle. 540 ÷ 5 = 108

Example 3 CYP A.144° B.225° C.1,440° D.1,800° ART An artist is creating a sculpture that is made up of regular decagons. Find the measure of an interior angle of a regular decagon.

A.120° B.360° C.720° D.1,080° Find the sum of the measures of the interior angles of a hexagon. Five Minute Check 1

A.140° B.1,080° C.1,260° D.1,620° Find the sum of the measures of the interior angles of a nonagon. Five Minute Check 2

A.120° B.135° C.180° D.1,080° Find the measure of one interior angle in a regular octagon. Round to the nearest tenth if necessary. Five Minute Check 3

A.154.3° B.180° C.2,160° D.2,520° Find the measure of one interior angle in a regular 14-gon. Round to the nearest tenth if necessary. Five Minute Check 4

A.173.6° B.176.8° C.186.7° D.9,720° Find the measure of one interior angle in a regular 56-gon. Round to the nearest tenth if necessary. Five Minute Check 5

A.m  X = 120°, m  Y = 20°, m  Z = 40° B. m  X = 120°, m  Y = 30°, m  Z = 30° C. m  X = 130°, m  Y = 20°, m  Z = 30° D. m  X = 110°, m  Y = 50°, m  Z = 20° Five Minute Check 6 The following statements are true about triangle XYZ.The measure of each angle is evenly divisible by 20.m  X is greater than m  Z.m  Z is greater than m  Y.m  Y + m  Z = m  X. What are the angle measures of triangle XYZ?