Question

△ABC is an isosceles triangle in which AB = AC. Sides BA is produced to D such that AD = AB. Find the measure of the ∠BCD.

• A. 30°
• B. 60°
• C. 90°
• D. 45°

Answer 1

The correct option is C 90°

In △ABC, we have

AB = AC (Given)

∠ACB = ∠ABC ... (1) (Since angles opp. to equal sides are equal.)

Now, AB = AD (Given)

∴AD = AC (Since AB = AC)

Thus , in △ADC, we have

AD = AC

⇒∠ACD = ∠ADC ... (2) (Since angles opp. to equal sides are equal.)

Adding (1) and (2) , we get

∠ACB + ∠ACD = ∠ABC + ∠ADC

⇒∠BCD = ∠ABC + ∠BDC (Since ∠ADC = ∠BDC)

⇒∠BCD + ∠BCD = ∠ABC + ∠BDC + ∠BCD (Adding ∠BCD on both sides.)

⇒2∠BCD = 180° (Angle sum property)

⇒∠BCD = 90°

Hence, ∠BCD is a right angle.