Question

In ATUV, TV is extended through point V to point W,

Answer 1

Answer:

m∠UVW = 53°

Step-by-step explanation:

From the picture attached,

m(∠VTU) = (x - 2)°

m(∠TUV) = (2x + 11)°

m(∠UVW) = (6x - 15)°

Since, ∠UVW is the exterior angle of the ΔTUV,

By the triangle sum theorem,

m∠VTU + m(∠TUV) + m(∠UVW) = 180°

(x - 2)° + (2x + 11)° + (6x - 15)° = 180°

9x - 6 = 180

9x = 186

x = $\frac{186}{9}$

x = $\frac{62}{3}$

By the property of exterior angle of a triangle,

m(∠UVW) = m(∠VTU) + m(TUV)

                = (x - 2) + (2x + 11)

                = 3x - 9

Now by substituting the value of x,

(3x - 9)° = $3(\frac{62}{3})-9$

           = 62 - 9

           = 53°

Therefore, m∠UVW = 53°