Question

If exterior angle of an isosceles triangle is 1100 and its interior opposite angles are equal, then each equal angle measures 

A.65 degree

B.60 degree

C.50 degree

D.55 degree​

Answer 1

Answer:

d) 55°

Explanation:

110°+x=180°

x=70°

sum of all sides of triangle =180°

so, 70°+y+z=180°

(here y=z given)

2y=110°

y=55°

Answer 2

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=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

.