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 X = Y, that means that you can substitute Y by X or vice versa.

You can work out two equations:
Since there are 180 degrees in a triangle, that means:
1: X + Y + Z = 180

Substitute Y by X:
1: X + X + Z = 180
1: 2X + Z = 180

We can also make another equation based on that angle Z is 4 times bigger than angle X:

2: Z = 4X

Now, let's put equation 2 into equation 1 by substituting Z by 4x:

2X + 4X = 180
6X = 180
X = 30

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

Z = 4X
Z = 4 * 30
Z = 120

X = Y to X=30 and Y = 30