Question

An exterior angle of a triangle is 105° and the two interior opposite angles
differ by 15°. The smaller of the two interior opposite angles is of measure

Answer 1

Answer:

The smaller of the two interior opposite angles is of measure 45°.

Step-by-step explanation:

Let, the larger of the interior opposite angles be x. And, the smaller one will be (x-15°).

Given,an exterior angle of a triangle is 105°.

We know, exterior angle is equal to the sum of interior opposite angles.

A.T.Q,

x + (x-15°) = 105°

⇒ x + x -15° = 105°

⇒ 2x -15° = 105°

⇒ 2x = (105+15)°

⇒ 2x = 120°

⇒ x  = ($\frac{120}{2}$)°

∴ x  = 60°

∴The larger of the interior opposite angles is 60°.

∴The smaller of the two interior opposite angles is (60 - 15)° = 45°.

The sum of the two interior opposite angles is (60 + 45)° = 105° which is equal to the exterior angle, so the calculation is correct.