Question

. One of the exterior angles of triangle is 100°. The interior opposite angles are equal to
each other. Find the measure of these equal interior opposite angles. give me the all answers​

Answer 1

Answer:

Using the theorem that if the side of a triangle is produced then the interior angle is equal to the sum of two interior opposite angles of the triangle.

Let ΔABC be a triangle where the side BC is produced.

By the theorem we have

∠A+∠B=100o …………..(1)

It is given that the interior opposite angles are equal i.e., ∠A=∠B.

∴ Equation (1) becomes

2∠A=100o

⇒∠A=50o

⇒∠B=50o

Using angle sum property of a triangle,

Sum of all angles of a triangle =180o

⇒∠A+∠B+∠C=180o

⇒100+∠C=180o [from (1)]

⇒∠C=180o−100o

⇒∠C=80o.

Hence ∠A=50o

∠B=50o

∠C=80o.