The interior angles of a pentagon are in the ratio 4 : 5 : 6 : 7 : 5. Find each angle of the pentagon.

According to the properties of polygons, if a polygon has n sides, then the sum of its interior angles is (2n - 4) x 90°.

A pentagon have 5 sides.

So, sum of its interior angles is:

(2 x 5 - 4) x 90°

= (10 - 4) x 90°

= 6 x 90°

= 540°

It is given that the interior angles of the pentagon are in the ratio 4 : 5 : 6 : 7 : 5. Let each angle be a.

So,

4a + 5a + 6a + 7a + 5a = 540°

⇒ 27a = 540°

⇒ a = $\dfrac{540°}{27}$

⇒ a = 20°

The angles are:

4a = 4 x 20° = 80°

5a = 5 x 20° = 100°

6a = 6 x 20° = 120°

7a = 7 x 20° = 140°

5a = 5 x 20° = 100°

Hence, the measures of the angles are 80°, 100°, 120°, 140° and 100°.