Question

In an isosceles triangle, each base angle is 30 degrees more than the vertex angle. What are the measures of the three angles?

Answer 1

`40°,70°,70°`

Explanation:

Notice that in an isosceles triangle there are at least two congruent angles. Also, as in all triangles, the sum of the angles is `180°`.

If we say the vertex angle is `x°`, we can say that each base angle is `(x+30)°`. We know that the angles' sum is `180°`, so we can write the following equation relating each of the angles:
`x+(x+30)+(x+30)=180`

We can then solve for `x` and determine that `3x+60=180`, which leads to `3x=120` and finally `x=40`, so the vertex angle is `40°` and each base angle is `70°`.