Question

Triangle ABC is an isosceles triangle with AB = BC and mA=75°.


What is mB?

Answer 1

Answer: 30 degrees

Explanation:

Answer 2

The correct answer is B)
`$75^(\circ)$`.

In an isosceles triangle, the two base angles are congruent.

So in this triangle,
`$\angle B=\angle C$`.

The sum of the angles in a triangle is
`$180^(\circ)$`, so we have:
`$ \angle A + \angle B + \angle C = 180^(\circ)$`.

Substituting in what we know about
`$\angle A$`, we get:

`$75^(\circ)+\angle B+\angle C=180^(\circ)$`

Since
`$\angle B=\angle C$`, we can rewrite this as:

`$75^(\circ)+2 \angle B=180^(\circ)$`

Solving for
`$\angle B$`, we get:
`$2 \angle B=105^(\circ)$`

Therefore
`$\angle B=(105^(\circ))/(2)=52.5^(\circ)$`

However, we know that
`$\angle B=\angle C$`, so
`$\angle C=52.5^(\circ)$` as well.

Therefore, the measure of
`$\angle B$` is
`$75^(\circ)$`.