Question

. ABC is an isosceles triangle with AB = AC. The vertex angle A measures eight times the
measure of a base angle. AD is the angle bisector of vertex angle A. What is the measure of
the angle BAD?

Answer 1

First find base angle THEN bisector angle

Answer 2

∠ BAD = 72°

Step-by-step explanation:

See the attached diagram.

Let the base angle is x degree i.e. ∠ B = ∠ C = x

So, the vertex angle is 8x degree i.e. ∠ BAC = 8x

Now, from Δ ABC, 8x + x + x = 180°

⇒ 10x = 180°

⇒ x = 18°

Hence, 8x = 8 × 18° = 144°

Now, as AD is the bisector of vertex angle ∠ BAC, so ∠ BAD will be half of ∠ BAC i.e. 144°.

So, ∠ BAD = $\frac{1}{2} \times 144^{\circ} = 72^{\circ}$ (Answer)