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Question
Find the angles of a pentagon which are in the ratio 4: 4: 6: 7: 6.
Solution
A pentagon has 5 sides
∴ Sum of interior angles
= (n - 2) x 180°
= (5 - 2) x 180°
= 3 x 180°
= 540°
Ratio of the angles
= 4: 4: 6: 7: 6
∴ The interior angles are 4x°, 4x°, 6x°, 7x° and 6x°.
∴ 4x° + 4x° + 6x° + 7x° + 6x° = 540°
⇒ 27x° = 540°
⇒ x° = 20°
The interior angles of the pentagon are 80°, 80°, 120 , 140° and 120°.
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