Question

An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of these equal angles is ______.

Options

• `37 1^circ/2`

• `52 1^circ/2`

• `72 1^circ/2`

• 75°

Answer 1

An exterior angle of a triangle is 105° and its two interior opposite angles are equal. Each of these equal angles is `underlinebb(52 1^circ/2)`.

Explanation:

Let one of interior angle be x°.

∴ Sum of two opposite interior angles = Exterior angle

∴ x° + x° = 105°

2x° = 105°

x° = `(105^circ)/2`

x° = `52 1^circ/2`

Hence, each angle of a triangle is `52 1^circ/2`.