Question

In ΔАВC, AB = AC and ∠BAC = 30°. Find the value of x.

Answer 1

Given: In triangle ABC, AB = AC isosceles and ∠BAC = 30°. 

BC is produced to D and x is the angle between AC and CD the exterior angle at C.

Step-wise calculation:

1. In an isosceles triangle, the base angles are equal.

So ∠ABC = ∠ACB

= `(180^circ - ∠BAC)/2`

2. Compute the base angles:

`∠ACB = (180^circ - 30^circ)/2`

= `150^circ/2`

= 75°

3. Angle x is the angle between AC and the extension CD of BC.

So x and the interior angle ∠ACB are supplementary: 

x = 180° – ∠ACB

= 180° – 75°

⇒ x = 105°