Question

I would like to draw an isosceles triangle with the vertex measuring 75 degrees. Whats is the measure of each base angle?

Answer 1

`52.5˚`

Explanation:

In an isosceles triangle, there are at least `2` congruent angles—the base angles.

Here's what we know:

The vertex angle is `75˚`.
The sum of the angles in a triangle is `180˚`.
The base angles are congruent.

If we call the measure of each base angle `x`, we can write the following equation relating the degree measures of all three angles in the triangle:

`x+x+75=180`

Therefore,

`2x+75=180`
`2x=105`
`x=52.5`

So, the vertex angle of this triangle is `75˚` and each base angle is `52.5˚`.