The exterior angles of a pentagon are in the ratio 1 : 2 : 3 : 4 : 5. Find its interior angles.

It is given that the exterior angles of a pentagon are in the ratio 1 : 2 : 3 : 4 : 5.

Let the exterior angles be a, 2a, 3a, 4a and 5a.

According to the properties of a polygon, the sum of the exterior angles is 360°.

⇒ a + 2a + 3a + 4a + 5a = 360°

⇒ 15a = 360°

⇒ a = $\dfrac{360°}{15}$

⇒ a = 24°

The exterior angles are,

= 24°, 2 x 24°, 3 x 24°, 4 x 24° and 5 x 24°

= 24°, 48°, 72°, 96° and 120°

The interior angles are calculated by subtracting the exterior angles from 180°:

180° - 24° = 156°

180° - 48° = 132°

180° - 72° = 108°

180° - 96° = 84°

180° - 120° = 60°

Hence, the interior angles are 60°, 84°, 108°, 132° and 156°.