Question

On circle O above the measure of arc SV is 120 degrees. What is the measure of arc VU.

Answer 1

Given:

On circle O, the measure of arc SV is 120° and m∠STU = 82°

We need to determine the measure of arc VU

Measure of arc VU:

The measure of arc VU can be determined using the inscribed angle theorem.

Thus, we have;

`m \angle STU=(1)/(2) m (\widehat{SU})`

The measure of SU is SU = SV + VU

Using this in the above formula, we get;

`m \angle STU=(1)/(2) (m \widehat{SV}+m \widehat{VU})`

Substituting m∠STU = 82° and
`m \widehat{S V}=120^(\circ)`, we have;

`82^(\circ)=(1)/(2)(120^(\circ)+m \widehat{VU})`

`164^(\circ)=120^(\circ)+m \widehat{VU}`

`44^(\circ)=m \widehat{VU}`

Hence, the measure of arc VU is 44°