Question

F 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°


2)
If 2a = 80 and b = c, what is the measure of ∠b?
A) 40°
B) 50°
C) 80°
D) 100°

Answer 1

Part 1) Option A.
`m\angle a=35^o`

Part 2) Option B.
`m\angle b=50^o`

Explanation:

we know that

An isosceles triangle has two equal sides and two equal angles

Part 1) what is the measure of ∠a?

we know that

`m\angle b=m\angle c` ----> equation A

Remember that the sum of the interior angles of triangle is equal to 180 degrees

we have

`m\angle b+m\angle c+2m\angle a=180^o` ----> equation B

substitute equation A in equation B

`m\angle c+m\angle c+2m\angle a=180^o`

`2m\angle c+2m\angle a=180^o`

Divide by 2 both sides

`m\angle c+m\angle a=90^o`

we have

`m\angle c=55^o` ---> given problem

substitute

`55^o+m\angle a=90^o`

`m\angle a=90^o-55^o=35^o`

Part b) we have that

we have

`2m\angle a=80^o` ---> given problem

`m\angle b=m\angle c` ---> equation A

Remember that the sum of the interior angles of triangle is equal to 180 degrees

we have

`m\angle b+m\angle c+2m\angle a=180^o` ----> equation B

substitute equation A in equation B

`m\angle b+m\angle b+2m\angle a=180^o`

`2m\angle b+2m\angle a=180^o`

we have

`2m\angle a=80^o`

substitute

`2m\angle b+80^o=180^o`

`2m\angle b=180^o-80^o`

`2m\angle b=100^o`

`m\angle b=50^o`