Question

In circle O, RT and SU are diameters.15x 8)10If mRV mVU, what is mVU?O 470O 5264°870

Answer 1

13x = 15x - 8
-15x

-2x = -8
/-2 /-2

x=4

15(4) - 8 = 52

52 - 180 =128

128/2 = 64

Answer 2

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\°`