Question

If h is an angle bisector of the given isosceles triangle, what is the measure of ∠a if ∠c = 55°?

A) 35°

B) 55°

C) 70°

D) 105°

Answer 1

It would be A) 35°....

Answer 2

Answer: A) 35°

Explanation:

In the given picture , we have an isosceles triangle , in which h is an angle bisector , divide an angle into two parts named as ∠a and ∠a.

∠c = 55°

We know that the angles opposite to the equal sides of an isosceles triangle are equal.

`\Rightarrow\ \angle{b}=\angle{c}=55^(\circ)`

By angle sum property , we have

`\angle{a}+\angle{a}+\angle{b}+\angle{c}=180^(\circ)`

`\Rightarrow\ 2\angle{a}+55^(\circ)+55^(\circ)=180^(\circ)`

`\Rightarrow\ 2\angle{a}=180^(\circ)-110^(\circ)`

`\Rightarrow\ 2\angle{a}=70^(\circ)`

`\Rightarrow\ \angle{a}=35^(\circ)` [Divide both sides by 2]

Hence, the correct answer is A) 35° .