In ΔUVW, start overline, U, W, end overlineUW is extended through point W to point X, m, angle, W, U, V, equals, left bracket, 2, x, plus, 15, right bracket, degreesm∠WUV=(2x+15)∘, m, angle, U, V, W, equals, left bracket, 2, x, plus, 15, right bracket, degreesm∠UVW=(2x+15)∘, and m, angle, V, W, X, equals, left bracket, 8, x, minus, 14, right bracket, degreesm∠VWX=(8x−14)∘. Find m, angle, W, U, V, .m∠WUV

1 answer

Since angles in a triangle add up to 180 degrees, we can set up the equation:

m∠WUV + m∠UVW + m∠VWX = 180 degrees

Substituting the given values, we have:

(2x + 15) + (2x + 15) + (8x - 14) = 180

Combining like terms, we get:

12x + 16 = 180

Subtracting 16 from both sides, we have:

12x = 164

Dividing by 12, we find:

x = 13.67

Therefore, m∠WUV = 2x + 15 = 2(13.67) + 15 = 42.34 degrees.