Question

In ΔWXY, start overline, W, Y, end overlineWY is extended through point Y to point Z, m, angle, Y, W, X, equals, left bracket, 2, x, plus, 9, right bracket, degreesm∠YWX=(2x+9)∘, m, angle, W, X, Y, equals, left bracket, 2, x, plus, 16, right bracket, degreesm∠WXY=(2x+16)∘, and m, angle, X, Y, Z, equals, left bracket, 8, x, plus, 1, right bracket, degreesm∠XYZ=(8x+1)∘. Find m, angle, W, X, Y, .m∠WXY

Answer 1

Since ∠WXY and ∠YWX are adjacent angles, they form a linear pair. Therefore, their sum is equal to 180 degrees.

(2x + 9) + (2x + 16) = 180
4x + 25 = 180
4x = 155
x = 38.75

m∠WXY = 2(38.75) + 9 = 86.5 degrees.