Question

Please help!

In the diagram shown, ABC is an equilateral triangle and ACD is an
isosceles triangle. What is the value of angle ADC?
(1) 30°
(2) 45°
(3) 60°
(4) 15°​

Answer 1

30°

Explanation:

Since ΔACD is isosceles with congruent sides AC = CD , then

∠ADC = ∠CAD

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

∠ACB is an exterior angle of ΔACD, hence

∠ACD + ∠CAD = 60° , thus

2 ∠ADC = 60 ( divide both sides by 2 )

∠ADC = 30°