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 = [tex]\frac{186}{9}[/tex]
x = [tex]\frac{62}{3}[/tex]
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)° = [tex]3(\frac{62}{3})-9[/tex]
= 62 - 9
= 53°
Therefore, m∠UVW = 53°
