Question

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?

Answer 1

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`