Question

each base angle of an isosceles triangle is 30 more than twice the measure of the vertex angle. what is the measure of the vertex angle.

Answer 1

The measure of the vertex angle is 24°

Explanation:

Suppose, the measure of the vertex angle
`=x`

It is given that each base angle of the isosceles triangle is 30 more than twice the measure of the vertex angle.

So, the measure of each base angle
`=2x+30`

That means, the measures of three angles in the triangle are
`x,\ \ 2x+30\ \ and\ \ 2x+30`.

Now we know, the sum of all three angles in any triangle is always 180°. So, the equation will be.....

`x+(2x+30)+(2x+30)=180`

`5x+60=180\\ \\ 5x=180-60\\ \\ 5x=120\\ \\ x=(120)/(5)=24`

So, the measure of the vertex angle is 24°