Question

find the value of x ​

Answer 1

Answer:

140°

Step-by-step explanation:

In ∆ABC

Two sides are equal

so,

<ACD +<BAC =180°

x° + 40° =180°

x°= 180°- 40°

x° = 140°

Answer 2

Answer:

110°

Step-by-step explanation:

In △ABC it is given that:

side AB = side AC

∠BAC = 40°

As two sides AB and AC are equal, it is an isosceles triangle.

We know that in an isosceles triangle, the two equal sides make two equal angles, i.e.

 ∠ABC = ∠ACB

By angle sum property of a triangle,

180° = 40 + ∠ABC + ∠ACB

or 180° = 40 + ∠ABC + ∠ABC (proved earlier)

⇒ 2 ∠ABC = 180° - 40°

⇒ 2 ∠ABC = 140°

⇒ ∠ABC = 70°

Finally by using exterior angle property of a triangle,  

∠x = ∠ABC + ∠BAC

⇒ ∠x = 70° + 40°

⇒ ∠x = 110°

Therefore, ∠x is 110°