Find the values of x and y.

Question

∆𝐿𝑀𝑁 ≅ ∆𝑃𝑄𝑅, 𝑚∠𝐿 = 40°, 𝑚∠𝑀 = 90°, 𝑚∠𝑃 = (17𝑥 − 𝑦)°, 𝑚∠𝑅 = (2𝑥 + 4𝑦)°

Answer 1

Assuming that you have named the similar triangles so that corresponding
angles are equal, that is
𝑚∠𝐿 = 𝑚∠𝑃 , etc
we have to match up 𝑚∠N with 𝑚∠𝑅

we know 2 of the angles of ∆𝐿𝑀𝑁, so 𝑚∠N = 180 - 40 - 90 = 50°

so 𝑚∠𝐿 = 𝑚∠𝑃
17x - y = 40 ----> y = 17x - 40
𝑚∠N with 𝑚∠𝑅
2x + 4y = 50
substitution:
2x + 4(17x-40) = 50
2x + 68 - 4x = 50
-2x = -18
x = 9
then y = 17(9) - 40 = 113°

check my arithmetic