Looking at the angle markers, we know that ∠A and ∠E as well as ∠B and ∠G are congruent angles. This means that each pair of angles has equal measures.
m∠A = m∠E
m∠B = m∠G
By the Third Angles Theorem, ∠C and ∠F also have the same measure. We can use these congruence relations to create equations that we can use to find the values of x and y.
m∠A = m∠E ⇔ 14=3x+y
m∠C = m∠F ⇔ 18=5x-y
From here, we can create a system of two equations.
14=3x+y & (I) 18=5x-y & (II)
To solve this system, we will use the Elimination Method.
