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 we know that the sum of the angles in a triangle is 180 degrees, we can write the equation:

m∠WUV + m∠UVW + m∠VWX = 180

Substituting the given angle measures into the equation, we have:

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

Combine like terms:

12x + 16 = 180

Subtract 16 from both sides:

12x = 164

Divide both sides by 12:

x = 13.67

Now substitute x back into the expression for m∠WUV:

m∠WUV = 2x + 15 = 2(13.67) + 15 = 42.34

Therefore, m∠WUV = 42.34 degrees.