Question

Find m∠UVT m∠WVU = 169° m∠WVT = (2x + 20)° m∠UVT = (3x + 19)° A) 91° B) 94° C) 97° D) 100°\

Answer 1

m ∠ UVT = 97° is the required answer.

Explanation:

Given:

m∠WVU = 169°

m∠WVT = (2x + 20)°

m∠UVT = (3x + 19)°

To Find:

m∠UVT = ?

Solution:

Angle Addition Postulate is that if you place two angles side by side, then the measure of the resulting angle will be equal to the sum of the two original angle measures.

So By applying this property in the diagram below we get,

m∠ WVT + m∠UVT = m∠WVU ............{Angle Addition Postulate}

`(2x+20) + (3x+19) = 169\\5x + 39 = 169\\5x=169-39\\5x=130\\\therefore x=(130)/(5) \\\therefore x=26\\`

Now,

m∠UVT = (3x + 19)°

Substituting x = 26 we get

m∠UVT = 3 ×26 + 19

= 78 +19

∴ m∠UVT = 97°