Question

One of the exterior angles of a triangle is 100⁰. The interior opposite angles are equal to each other.What will be the measure of these equal interior opposite angles
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Answer 1

Answer:

The equal interior opposite angles = x

x + x = 100⁰ (Exterior angle property - sum of interior opp. angles is exterior angle)

2x = 100⁰

x = 100⁰/2

x = 50⁰

∴ Both the interior angles = 50⁰

Answer 2

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.