To find the values of the variables, the first thing we need to remember is the Triangle Angle-Sum Theorem.
Triangle Angle-Sum Theorem
The sum of the interior angles of a triangle is 180^(∘).
Using this theorem, we can write the following.
m∠X+ m∠Y+ m∠W=180
⇓
(6y-2)+(4x+20)+52=180
Now, by the given markings, we can see that WX≅WY.
By the Isosceles Triangle Theorem, we know that if two sides of a triangle are congruent, then the angles opposite those sides are congruent. With this theorem in mind, we can conclude that ∠X ≅ ∠Y and that their measures are equal.
m∠X =& m ∠Y
⇓
6y-2=& 4x+20
Knowing that these expressions are equal, we can substitute one for the other in our equation created by the Interior Angles Theorem. Let's first find the value of x.
Finally, we can find the value of y by substituting x=11 into either known equation. For simplicity, we will use the equation relating the side lengths.
