ABC , is an isosceles triangle such that AB = AC and AD is the median to base BC . Then, ∠ BAD =

Question

ABC , is an isosceles triangle such that AB = AC and AD is the median to base BC . Then, &#x2220; BAD =

Philoid · Accepted Answer

For an isosceles triangle ∠ABC = ∠ACB = 35°

Let the ∠ADB be x

Then,

∠ADC = 180^o - x

As AD is median so BD = CD

And for isosceles triangle AB = AC

So,

= = 1

By angle bisector theorem,

∠BAD = ∠CAD = y (Let)

For BAD

35 + x + y =180 (i)

For DAC

35 + 180 – x + y = 180 (ii)

35 + y = x

Therefore,

35 + 34 + y + y = 180^o

2y + 70 = 180^o

2y = 100^o

y = 55^o

Therefore,

∠BAD = ∠CAD = 55^o