Question

In an isosceles triangle ABC, the measure of equal angles ∠ABC and ∠ACB are 55°. If AD is median of the triangle on BC then what is the value of ∠BAD?

1. 35° 
2. 45° 
3. 25° 
4. 55° 

Answer 1

Correct Answer - Option 1 : 35° 

Given:

ABC is an isosceles triangle

∠ABC and ∠ACB are 55°

AD is the median of the given triangle

Concept used:

The median of an isosceles triangle is perpendicular bisector of the unequal opposite side and also an angle bisector.

Calculation:

In given triangle ABC, ∠ABC and ∠ACB are 55°

Using angle sum property of the triangle

⇒ ∠BAC + ∠ABC + ∠ACB = 180°

⇒ ∠BAC + 55° + 55° = 180°

⇒ ∠BAC = 70°

Using concept, we get

∠BAD = ∠DAC

⇒ ∠BAD + ∠DAC = ∠BAC

⇒ 2∠BAD = ∠BAC

⇒ 2∠BAD = 70°

⇒ ∠BAD = 35°

∴ The value of ∠BAD is 35°.