Question

If an exterior angle of a triangle is 65° and one of the opposite interior angle to it is 35° then other two angles are 100° and 80°, 30° and 85° ,30° and 115°, 100° and 30°​

Answer 1

Step-by-step explanation:

Solution

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=100

o

…………..(1)

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

∴ Equation (1) becomes

2∠A=100

o

⇒∠A=50

o

⇒∠B=50

o

Using angle sum property of a triangle,

Sum of all angles of a triangle =180

o

⇒∠A+∠B+∠C=180

o

⇒100+∠C=180

o

[from (1)]

⇒∠C=180

o

−100

o

⇒∠C=80

o

.

Hence ∠A=50

o

∠B=50

o

∠C=80

o

.