m∠U=11°
Step-by-step 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\°](/tpl/images/0394/9479/0b45a.png)
solve for x
Combine like terns left side
![(13x-2)=180](/tpl/images/0394/9479/9fd7f.png)
Adds 2 both sides
![13x=182](/tpl/images/0394/9479/a174e.png)
divide by 13 both sides
![x=14](/tpl/images/0394/9479/9615d.png)
Find the measure of angle U
m∠U = (2x-17)°
substitute the value of x
m∠U = (2(14)-17)=11°