Question

In ΔUVW, m∠U = (2x-17)^{\circ}(2x−17)

∘

, m∠V = (7x+16)^{\circ}(7x+16)

∘

, and m∠W = (4x-1)^{\circ}(4x−1)

∘

. Find m∠U.

Answer 1

m∠U=11°

Explanation:

we know that

The sum of the interior angles in a triangle must be equal to 180 degrees

so

In this problem

m∠U+m∠V+m∠W=180°

substitute the given values

`(2x-17)\°+(7x+16)\°+(4x-1)\°=180\°`

solve for x

Combine like terns left side

`(13x-2)=180`

Adds 2 both sides

`13x=182`

divide by 13 both sides

`x=14`

Find the measure of angle U

m∠U = (2x-17)°

substitute the value of x

m∠U = (2(14)-17)=11°