Answer:
Arc VU = 44°
Step-by-step explanation:
Given:
Arc SV means ∠SOV = 120°
Arc VU means ∠VOU = ?
We know that, from central angle theorem, central angle made by arc is twice the angle made the same arc at the circumference.
∴ ∠SOU = 2 × ∠STU
⇒ ∠SOU = 2(82°)
⇒ ∠SOU = 164°
Now, from angle addition theorem,
∠SOU = ∠SOV + ∠VOU
⇒ 164° = 120° + ∠VOU
⇒ 164° - 120° = ∠VOU
⇒ ∠VOU = 44°
Therefore, the measure of the arc VU is 44°.
