Question

Determine the measure of ∠UVS.
A) 19.5°
B) 39°
C) 78°
D) 102°

Answer 1

(B)
`{\angle}UVS=39^(\circ)`

Explanation:

Given: A circle with intercepted arc is
`78^(\circ)`.

To find: The measure of ∠UVS.

Solution:

Since, we know that the angle made of the inscribed angle is half of the intercepted arc, therefore

`Inscribed angle=(1)/(2)Intercepted arc` (1)

We are given that A circle with intercepted arc is
`78^(\circ)`, thus equation (1) becomes:

`{\angle}UVS=(1)/(2)arc US`

`{\angle}UVS=(1)/(2)(78^(\circ))`

`{\angle}UVS=39^(\circ)`

Therefore, option B is correct.

Answer 2

The inside angle ( UVS) is equal to 1/2 the outside angle given.

UVS = 1/2(78)

UVS = 39 degrees

The answer is B.