# 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.

**Q2: **

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

**Q4: **

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

**Q5: **

From the information in the figure, what is ?

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**Q7: **

Calculate .

**Q8: **

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

**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.

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**Q16: **

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

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**Q17: **

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

**Q20: **

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

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**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.