Question

An exterior angle of a triangle is equal to 100° and two interior opposite angles are equal. Each of these angles is equal to

Options

• 75°

• 80°

• 80°

• 40°

• 50°

Answer 1

n the ΔABC, CD is the ray extended from the vertex C of ΔABC. It is given that the exterior angle of the triangle is  100° and two of the interior opposite angles are equal.

So, ∠ACD = 100° and _{A = ∠B}

So, now using the property, “an exterior angle of the triangle is equal to the sum of the two opposite interior angles”, we get.

In ΔABC

∠A + ∠B = ∠ACD

∠2A = 100°

`∠A =  (100°)/2`

∠A = 50°

∠A = ∠B = 50°

Therefore, each of the two opposite interior angles is 50°.