Geometry and measuresKey Stage 3

Angles in a polygon with algebra

Use polygon angle facts to find missing values.

  • Find the interior-angle sum from the number of sides.
  • Add the given numbers and expressions, set them equal to the total, then solve.

Example 1

Find the value of .

The 5 interior angles add to 540°.Apply this to both sides.Apply this to both sides.
The 5 interior angles add to 540°.
Apply this to both sides.Apply this to both sides.

Example 2

Find the value of .

The 6 interior angles add to 720°.Apply this to both sides.Apply this to both sides.
The 6 interior angles add to 720°.
Apply this to both sides.Apply this to both sides.

Your turn

Question 1

Find the value of .

Check answer
The 5 interior angles add to 540°.Apply this to both sides.Apply this to both sides.
The 5 interior angles add to 540°.
Apply this to both sides.Apply this to both sides.
Question 2

Find the value of .

Check answer
The 6 interior angles add to 720°.Apply this to both sides.Apply this to both sides.
The 6 interior angles add to 720°.
Apply this to both sides.Apply this to both sides.
Question 3

Find the value of .

Check answer
The 5 interior angles add to 540°.Apply this to both sides.Apply this to both sides.
The 5 interior angles add to 540°.
Apply this to both sides.Apply this to both sides.
Question 4

Find the value of .

Check answer
The 6 interior angles add to 720°.Apply this to both sides.Apply this to both sides.
The 6 interior angles add to 720°.
Apply this to both sides.Apply this to both sides.
Question 5

Find the value of .

Check answer
The 5 interior angles add to 540°.Apply this to both sides.Apply this to both sides.
The 5 interior angles add to 540°.
Apply this to both sides.Apply this to both sides.
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