a. x = 50, the measure of ∠A = 170°.
b. y = 7, the measure of FE = 14, AB = 14.
In the question, we are given that ΔABC ≅ ΔEFG, that is, triangle ABC is congruent to triangle EFG.
As we know that corresponding parts of congruent triangles are also congruent,
we can write that:
∠A = ∠E,
∠B = ∠F,
∠C = ∠G,
AB = EF,
BC = FG, and
CA = GE.
Now,
a. We are asked to solve for x.
We know that:
∠A = ∠E,
or, 3x + 20 = 5x - 80,
or, 3x - 5x = -80 - 20,
or, -2x = -100,
or, x = -100/-2 = 50.
Also, we are asked to find the measure of ∠A.
∠A = (3x + 20)° = (3*50 + 20)° = 170°.
b. We are asked to solve for y.
We know that,
AB = EF,
or, y + 7 = 3y - 7,
or, y - 3y = - 7 - 7,
or, -2y = -14,
or, y = -14/-2 = 7.
Also, we are asked to find the measure of FE and AB.
FE = 3y - 7 = 3*7 - 7 = 14.
AB = y + 7 = 7 + 7 = 14.
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