In a triangle ABC, AB = AC. BC is extended to D such that CD = AB and the angle ADC is 30°. What are the angles of triangle ABC?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is otpion 3 i.e. 60°, 60°, 60°
The base angles are equal in an isosceles triangle.
AB = AC
So, the triangle ABC is isosceles.
∠B = ∠C
In triangle ADC, we know CD = AB, and ∠ADC = 30°.
The sum of angles in any triangle = 180°.
Sum of the other two angles in triangle ADC = 180° - 30° = 150°
∠DAC = ∠DCA = 150°/2 = 75°
Now, ∠A + ∠B + ∠C = 180°
⇒ ∠B + ∠C = 180° - ∠A = 180° - 60° = 120°
⇒ ∠B = ∠C = 120°/2 = 60°
Therefore, the angles of triangle ABC are 60°, 60°, and 60°.