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# The Interior Angles of a Pentagon Are in the Ratio 4 : 5 : 6 : 7 : 5. Find Each Angle of the Pentagon. - Mathematics

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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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#### APPEARS IN

Selina Concise Mathematics Class 8 ICSE
Chapter 16 Understanding Shapes
Exercise 16 (A) | Q 8 | Page 181
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