Worksheet: Sum of the Interior Angles of a Polygon

Practice

In this worksheet, we will practice finding the sum of the interior angles of a polygon given the number of its sides.

Q1:

In the following figure, what is 𝑚 ∠ 𝐹 𝐴 𝐵 in the hexagon 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 ?

Q2:

In the figure, if 𝑚 ∠ 𝐴 = 1 3 7 ∘ , 𝑚 ∠ 𝐵 = 7 8 ∘ , 𝑚 ∠ 𝐶 = 1 1 3 ∘ , and 𝑚 ∠ 𝐸 = 1 3 1 ∘ , find 𝑚 ∠ 𝐷 .

Q3:

Given that 𝐴 𝐵 𝐶 𝐷 𝐸 is a regular pentagon, find 𝑚 ∠ 𝐴 𝐵 𝑋 .

Q4:

In the figure, segments 𝐸 𝐷 and 𝐵 𝐺 meet at 𝐴 . If 𝑚 ∠ 𝐹 = 9 0 ∘ , 𝑚 ∠ 𝐺 = 9 7 ∘ , 𝑚 ∠ 𝐸 = 9 7 ∘ , 𝑚 ∠ 𝐷 = 1 3 7 ∘ , and 𝑚 ∠ 𝐶 = 9 5 ∘ , find 𝑚 ∠ 𝐵 .

Q5:

From the information in the figure, what is 𝑚 ∠ 𝐶 𝐷 𝐸 ?

  • A 6 7 ∘
  • B 1 4 1 ∘
  • C 1 0 3 ∘

Q6:

The measures of the interior angles of a pentagon satisfy the ratio 3 ∶ 4 ∶ 4 ∶ 4 ∶ 5 . What is the measure of the smallest angle?

Q7:

Calculate 𝑚 ∠ 𝐵 + 𝑚 ∠ 𝐶 .

Q8:

The interior angles of a triangle are in the ratio 3 ∶ 4 ∶ 8 . What is the smallest angle?

  • A 9 6 ∘
  • B 1 2 ∘
  • C 4 8 ∘
  • D 3 6 ∘

Q9:

Given that 𝐴 𝐵 𝐶 𝐷 𝐸 is a regular pentagon, find 𝑚 ∠ 𝐴 𝐵 𝑋 .

Q10:

Given that 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 is a regular hexagon, find 𝑚 ∠ 𝐴 𝐵 𝑋 .

Q11:

Given that 𝐴 𝐵 𝐶 𝐷 𝐸 𝐹 is a regular hexagon, find 𝑚 ∠ 𝐴 𝐵 𝑋 .

Q12:

In the figure, if 𝑚 ∠ 𝐴 = 9 4 ∘ , 𝑚 ∠ 𝐵 = 1 0 1 ∘ , 𝑚 ∠ 𝐶 = 1 2 7 ∘ , and 𝑚 ∠ 𝐸 = 1 4 9 ∘ , find 𝑚 ∠ 𝐷 .

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