# Triangle XYZ is isosceles. The base angles, angle X and angle Y, are four times the measure of the vertex angle, angle Z. What is the measure of angle X?

##### 1 Answer

Nov 14, 2015

Set up two equations with two unknowns

You will find X and Y = 30 degrees, Z = 120 degrees

#### Explanation:

You know that

You can work out two equations:

Since there are 180 degrees in a triangle, that means:

Substitute

We can also make another equation based on that angle

Now, let's put equation 2 into equation 1 by substituting

Insert this value of X into either the first or the second equation (let's do number 2):