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 π‘šβˆ πΉπ΄π΅ in the hexagon 𝐴𝐡𝐢𝐷𝐸𝐹?

Q2:

In the figure, if π‘šβˆ π΄=137∘, π‘šβˆ π΅=78∘, π‘šβˆ πΆ=113∘, and π‘šβˆ πΈ=131∘, find π‘šβˆ π·.

Q3:

Given that 𝐴𝐡𝐢𝐷𝐸 is a regular pentagon, find π‘šβˆ π΄π΅π‘‹.

Q4:

In the figure, segments 𝐸𝐷 and 𝐡𝐺 meet at 𝐴. If π‘šβˆ πΉ=90∘, π‘šβˆ πΊ=97∘, π‘šβˆ πΈ=97∘, π‘šβˆ π·=137∘, and π‘šβˆ πΆ=95∘, find π‘šβˆ π΅.

Q5:

From the information in the figure, what is π‘šβˆ πΆπ·πΈ?

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 π‘šβˆ π΅+π‘šβˆ πΆ.

Q8:

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

Q9:

Given that 𝐴𝐡𝐢𝐷𝐸𝐹 is a regular hexagon, find π‘šβˆ π΄π΅π‘‹.

Q10:

Given that 𝐴𝐡𝐢𝐷𝐸𝐹 is a regular hexagon, find π‘šβˆ π΄π΅π‘‹.

Q11:

Given that 𝐴𝐡𝐢𝐷𝐸 is a regular pentagon, find π‘šβˆ π΄π΅π‘‹.

Q12:

In the figure, if π‘šβˆ π΄=140∘, π‘šβˆ π΅=65∘, π‘šβˆ πΆ=120∘, and π‘šβˆ πΈ=131∘, find π‘šβˆ π·.

Q13:

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

Q14:

Noah 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.

  • A2𝑛×90∘
  • B(π‘›βˆ’2)Γ—1802∘
  • C(π‘›βˆ’2)Γ—1802π‘›βˆ˜
  • D𝑛×90∘
  • E(π‘›βˆ’2)Γ—180∘

Q16:

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

  • A(π‘›βˆ’2)Γ—90π‘›βˆ˜
  • B180Γ—(π‘›βˆ’1)∘
  • C(π‘›βˆ’2)Γ—180π‘›βˆ˜
  • D(π‘›βˆ’2)Γ—1802∘

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 π‘₯ and 𝑦.

  • Aπ‘₯=45∘, 𝑦=135∘
  • Bπ‘₯=157.5∘, 𝑦=22.5∘
  • Cπ‘₯=135∘, 𝑦=45∘
  • Dπ‘₯=22.5∘, 𝑦=157.5∘

Q20:

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

  • A840β€²βˆ˜
  • B1680β€²βˆ˜
  • C420β€²βˆ˜
  • D1740β€²βˆ˜

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 π‘šβˆ π‘₯.

Q23:

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

Q24:

Given that 𝐴𝐡𝐢𝐷 is a square, find, in degrees, the values of π‘₯ and 𝑦.

  • Aπ‘₯=37∘, 𝑦=143∘
  • Bπ‘₯=127∘, 𝑦=37∘
  • Cπ‘₯=45∘, 𝑦=127∘
  • Dπ‘₯=37∘, 𝑦=127∘

Q25:

In the diagram below, what is the measure of angle 𝐴𝐡𝐢?

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