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