Question

In the given figure, AD is a median of ΔABC. If AB = AC and ∠BAD = 25°, then the measure of ∠ABC is equal to

• A. 60°
• B. 50°
• C. 65°
• D. 48°

Answer 1

The correct option is C 65°

In ΔADB and ΔADC,
AB = AC (Given)
BD = DC (Given)
AD = AD (Common)
∴ ΔADB ≅ ΔADC (SSS congruence rule)
⇒ ∠ADB = ∠ADC
Also, ∠ADB + ∠ADC = 180° (Linear pair)
⇒ ∠ADB = ∠ADC = 90°
In ΔADB,
∠ADB + ∠BAD + ∠ABD = 180° (Angle sum property)
⇒ 90° + 25° + ∠ABD = 180°
⇒ ∠ABD = 65°
⇒ ∠ABC = 65°
Hence, the correct answer is option (c).