Sum
The interior angles of a pentagon are in the ratio 4 : 5 : 6 : 7 : 5. Find each angle of the pentagon.
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Solution
Let the interior angles of the pentagon be 4x, 5x, 6x, 7x, 5x.
Their sum = 4x + 5x + 6x + 7x + 5x = 21x
Sum of interior angles of a polygon = (n - 2) × 180°
= (5 - 2) × 180°
= 540°
∴ 27x = 540
⇒ x = `540/27`
⇒ x = 20°
∴ Angles are 4 × 20° = 80°
5 × 20° = 100°
6 × 20° = 120°
7 × 20° = 140°
5 × 20° = 100°
Concept: Sum of Angles of a Polynomial
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