# Worksheet: Interior Angles of a Polygon

In this worksheet, we will practice finding the sum of the interior angles of a polygon given the number of its sides and the measure of an angle in a regular polygon.

Q1:

In the following figure, what is in the hexagon ? Q2:

In the figure, if , , , and , find . Q3:

Given that is a regular pentagon, find . Q4:

In the figure, segments and meet at . If , , , , and , find . Q5:

From the information in the figure, what is ? Q6:

The measures of the interior angles of a pentagon satisfy the ratio . What is the measure of the smallest angle?

Q7:

Calculate . Q8:

The interior angles of a triangle are in the ratio . What is the smallest angle?

Q9:

Given that is a regular hexagon, find . Q10:

Given that is a regular hexagon, find . Q11:

Given that is a regular pentagon, find . Q12:

In the figure, if , , , and , find . Q13:

Find the measure of one interior angle of a regular polygon that has 5 sides.

Q14:

Anthony finds a building that has a triangular base. If he were to walk around the building, finishing at the same point, in the same direction, how many degrees would he turn?

Q15:

Write an expression for the sum of the measures of the interior angles of a polygon with sides.

• A
• B
• C
• D
• E

Q16:

What is the fomula for the measure of the interior angle of a regular polygon with sides?

• A
• B
• C
• D

Q17:

What is the measure of the interior angle of a regular pentagon?

Q18:

Each interior angle of a polygon is . How many sides does it have?

Q19:

Find and . • A,
• B,
• C,
• D,

Q20:

Determine, to the nearest minute, the measure of the interior angle of a regular polygon that has 30 sides.

• A
• B
• C
• D

Q21:

A certain company makes hot tubs in a variety of different shapes. Find the measure of an interior angle of the regular nonagon model.

Q22:

This is a regular polygon. Find . Q23:

What is the sum of the interior angles of a hexagon?

Q24:

Given that is a square, find, in degrees, the values of and . • A,
• B,
• C,
• D,