Question

The interior angles of a triangle are in the ratio 1 : 2 : 3, then the ratio of its exterior angles is 3 : 2 : 1.

विकल्प

• True

• False

Answer 1

This statement is False.

Explanation:

Given, ratio of interior angles = 1 : 2 : 3

Let the interior angles be x, 2x and 3x.

So, x + 2x + 3x = 180°   ...[Angle sum property of triangle]

⇒ 6x = 180°

⇒ x = `180^circ/6` = 30°

∴ The interior angles are 30°, 60° and 90°.

Now, the exterior angles will be (180° – 30°), (180° – 60°) and (180° – 90°), i.e. 150°, 120° and 90°.

The ratio of exterior angles = 150° : 120° : 90°

= 15 : 12 : 9

= 5 : 4 : 3