Question

A base of an isosceles triangle is twice the measure of its vertex. What are the measures of its three angles?

Answer 1

Base angles: 72 degrees each

Vertex angle: 36 degrees

Let's call the measure of the base angle "x" and the measure of the vertex angle "y". We know that the base of the triangle is twice the measure of the vertex, so:

x = 2y

We also know that the sum of the angles in any triangle is 180 degrees. Since we have two base angles and one vertex angle, we can set up the equation:

2x + y = 180

Now, we can substitute the first equation (x = 2y) into the second equation:

2(2y) + y = 180

Simplifying the equation:

4y + y = 180

Combining like terms:

5y = 180

Dividing both sides by 5 to find y:

y = 36

Now that we know y, we can find x:

x = 2y

x = 2(36)

x = 72

Therefore, the measures of the three angles are: