8.7 PolygonsI can identify regular and not regular

polygons and find the angle measurements of regular polygons

ReviewThe lengths of three sides of a triangle are given. Classify the triangle.

1. 12, 12, 12

2. 18, 10, 14

3. 15, 15, 26

equilateral

scalene

isosceles

Vocabulary

polygonregular polygondiagonal

A polygon is a closed plane figure formed by three or more line segments. A regular polygon is a polygon in which all sides are congruent and all angles are congruent.

Polygons are named by the number of their sides and angles.

You can divide any quadrilateral into two triangles by drawing a diagonal, a line segment that connects two non-adjacent vertices. The sum of the interior angle measures in a triangle is 180°, so the sum of the interior angle measures in a quadrilateral is 360°.

Tell whether each shape is a polygon. If so, give its name and tell whether it appears to be regular or not regular.

polygon pentagon not regular

Tell whether each shape is a polygon. If so, give its name and tell whether it appears to

be regular or not regular.

octagon regularpolygon

Tell whether each shape is a polygon. If so, give its name and tell whether it appears to be regular or not regular.

quadrilateral regular

Tell whether each shape is a polygon. If so, give its name and tell whether it appears to be regular or not regular.

quadrilateral not regular

720°

The prefixes in the names of the polygons tell you how many sides and angles there are.

tri- = three quad- = four

penta- = five hexa- = six octa- = eight

Reading Math

1. Name each polygon and tell whether it appears to be regular or not regular.

2. What is the measure of each angle in a regular

dodecagon (12-sided figure)?

150°

nonagon, regular; octagon, not regular

1. Name the polygon and tell whether it appears to be regular or not regular.

A. pentagon, not regular

B. hexagon, regular

C. heptagon, regular

D. octagon, not regular

2. What is the measure of each angle in a regular decagon (10-sided figure)?

A. 108

B. 144

C. 150

D. 140

• What is the exterior angle of a polygon? • What do the exterior angles of a regular polygon add up to?

Square

The four angles create 360°

360 ÷ 4 = 90°

Exterior angle is 90°

REGULAR PENTAGON

The five angles create 360°

360 ÷ 5 = 72°

Exterior angle is 72°

Exterior angle =

360° ÷ number of angles

EXERCISES Calculate the angles marked with letters

100°

66°

A

98°91°

80°

75°

B 95°

90°

57°

33°25°

85°

C