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?

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Answer 1 · 2015-11-14T13:03:08

Set up two equations with two unknowns
You will find X and Y = 30 degrees, Z = 120 degrees

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#