Answer:
<em>The measure of the vertex angle is 24°</em>
Step-by-step explanation:
Suppose, the measure of the vertex angle ![=x](https://tex.z-dn.net/?f=%3Dx)
It is given that each base angle of the isosceles triangle is <u>30 more than twice the measure of the vertex angle</u>.
So, <u>the measure of each base angle</u> ![=2x+30](https://tex.z-dn.net/?f=%3D2x%2B30)
That means, the measures of three angles in the triangle are
.
Now we know, <u>the sum of all three angles in any triangle is always 180°</u>. So, the equation will be.....
![x+(2x+30)+(2x+30)=180](https://tex.z-dn.net/?f=x%2B%282x%2B30%29%2B%282x%2B30%29%3D180)
![5x+60=180\\ \\ 5x=180-60\\ \\ 5x=120\\ \\ x=\frac{120}{5}=24](https://tex.z-dn.net/?f=5x%2B60%3D180%5C%5C%20%5C%5C%205x%3D180-60%5C%5C%20%5C%5C%205x%3D120%5C%5C%20%5C%5C%20x%3D%5Cfrac%7B120%7D%7B5%7D%3D24)
So, the measure of the vertex angle is 24°