Polygon Unit Review - Angle Sum

Polygon Unit Review

Unit 7 Test Review

What is a polygon?

• Closed plane figure with 3 or more sides

• Sides may not cross

• Convex: Any diagonal will be interior

• Concave: One or more diagonals will be exterior

Multiple Select

Which of these are polygons?

Multiple Select

Which of these polygons are concave?

Angle Sum (n is the number of sides)

• The interior angle sum of a polygon is given by the formula  $S=\left(n-2\right)180\degree$  

• Each interior angle of a regular polygon is given by the formula  $A=\frac{\text{}\left(n-2\right)180\degree}{\text{n}}$  

Regular 15-gon

• Identify total angle sum

• Determine the measure of each angle.

Exterior Angle Sum of a Polygon

• The exterior angle sum for any polygon is  $360\degree$ .

• You can find missing angles if you know all but one of the exterior angles.

Multiple Choice

Find the missing exterior angle measure for this figure.

• 93°

• 115°

• 123°

• 144°

Multiple Choice

What is the angle sum for a 42-gon?

• 7200°

• 7560°

• 7920°

Multiple Choice

What is the measure of an interior angle of a regular 45-gon?

• 165°

• 170°

• 172°

• 172.8°

Multiple Choice

What is the value of x in the following?

• 58°

• 116°

• 122°

• 244°

Multiple Choice

What is the value of x in this image? (Hint: Find the interior angle sum for the quadrilateral first).

• 34°

• 124°

• 146°

• 214°

Multiple Choice

What is the area of this regular polygon?

• 294.75

• 353.7

• 436.23

• 589.5