Question

One exterior angle of a triangle is (10x - 16)০ and two interior opposite angles are (3x + 20)০ & (4x)০. Find the value of x.

Answer 1

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.