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 𝑚𝐹𝐴𝐵 in the hexagon 𝐴𝐵𝐶𝐷𝐸𝐹?

Q2:

In the figure, if 𝑚𝐴=137, 𝑚𝐵=78, 𝑚𝐶=113, and 𝑚𝐸=131, find 𝑚𝐷.

Q3:

Given that 𝐴𝐵𝐶𝐷𝐸 is a regular pentagon, find 𝑚𝐴𝐵𝑋.

Q4:

In the figure, segments 𝐸𝐷 and 𝐵𝐺 meet at 𝐴. If 𝑚𝐹=90, 𝑚𝐺=97, 𝑚𝐸=97, 𝑚𝐷=137, and 𝑚𝐶=95, find 𝑚𝐵.

Q5:

From the information in the figure, what is 𝑚𝐶𝐷𝐸?

  • A 1 0 3
  • B 6 7
  • C 1 4 1

Q6:

The measures of the interior angles of a pentagon satisfy the ratio 34445. What is the measure of the smallest angle?

Q7:

Calculate 𝑚𝐵+𝑚𝐶.

Q8:

The interior angles of a triangle are in the ratio 348. What is the smallest angle?

Q9:

Given that 𝐴𝐵𝐶𝐷𝐸𝐹 is a regular hexagon, find 𝑚𝐴𝐵𝑋.

Q10:

Given that 𝐴𝐵𝐶𝐷𝐸𝐹 is a regular hexagon, find 𝑚𝐴𝐵𝑋.

Q11:

Given that 𝐴𝐵𝐶𝐷𝐸 is a regular pentagon, find 𝑚𝐴𝐵𝑋.

Q12:

In the figure, if 𝑚𝐴=140, 𝑚𝐵=65, 𝑚𝐶=120, and 𝑚𝐸=131, find 𝑚𝐷.

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 𝑛 sides.

  • A 2 𝑛 × 9 0
  • B ( 𝑛 2 ) × 1 8 0 2
  • C ( 𝑛 2 ) × 1 8 0 2 𝑛
  • D 𝑛 × 9 0
  • E ( 𝑛 2 ) × 1 8 0

Q16:

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

  • A ( 𝑛 2 ) × 9 0 𝑛
  • B 1 8 0 × ( 𝑛 1 )
  • C ( 𝑛 2 ) × 1 8 0 𝑛
  • D ( 𝑛 2 ) × 1 8 0 2

Q17:

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

Q18:

Each interior angle of a polygon is 179. How many sides does it have?

Q19:

Find 𝑥 and 𝑦.

  • A 𝑥 = 4 5 , 𝑦 = 1 3 5
  • B 𝑥 = 1 5 7 . 5 , 𝑦 = 2 2 . 5
  • C 𝑥 = 1 3 5 , 𝑦 = 4 5
  • D 𝑥 = 2 2 . 5 , 𝑦 = 1 5 7 . 5

Q20:

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

  • A 8 4 0
  • B 1 6 8 0
  • C 4 2 0
  • D 1 7 4 0

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 𝑚𝑥.

Q23:

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

  • A 1 , 0 8 0
  • B 5 4 0
  • C 9 0 0
  • D 7 2 0

Q24:

Given that 𝐴𝐵𝐶𝐷 is a square, find, in degrees, the values of 𝑥 and 𝑦.

  • A 𝑥 = 3 7 , 𝑦 = 1 4 3
  • B 𝑥 = 1 2 7 , 𝑦 = 3 7
  • C 𝑥 = 4 5 , 𝑦 = 1 2 7
  • D 𝑥 = 3 7 , 𝑦 = 1 2 7

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