Worksheet: Interior Angles and Number of Sides of a Polygon

In this worksheet, we will practice finding the values of interior angles of a polygon given the number of its sides and vice versa.

Q1:

Find 𝑥 and 𝑦 .

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

Q2:

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

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

Q3:

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

Q4:

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

Q5:

Each interior angle of a polygon is 1 7 9 . How many sides does it have?

Q6:

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 2
  • D ( 𝑛 2 ) × 1 8 0 𝑛

Q7:

Shady 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?

Q8:

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

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

Q9:

Each interior angle of a polygon is 6 0 . How many sides does it have?

Q10:

Each interior angle of a polygon is 1 4 4 . How many sides does it have?

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