Step 1
Find the measure of angle x
we know that
[tex](13x)\°=(15x-8)\°[/tex] ------> by vertical angles
solve for x
[tex]13x=15x-8\\15x-13x=8\\2x=8\\x=4\°[/tex]
Step 2
Find the measure of arc VU
we know that
the measure arc RV is equal to the angle ROV-------> by central angle
the measure arc VU is equal to the angle VOU-------> by central angle
angle ROV=angle VOU-------> given problem
Let
y--------> angle VOU
[tex](2y)\°+(15x-8)\°=180\°[/tex]
Substitute the value of x and find the value of y
[tex](2y)\°+(15*4-8)\°=180\°[/tex]
[tex](2y)\°+(52)\°=180\°[/tex]
[tex](2y)\°=180\°-52\°[/tex]
[tex]y=64\°[/tex]
therefore
the answer is
the measure of the arc VU is equal to [tex]64\°[/tex]
