Question

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

Answer 1

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

UVS = 1/2(78)

UVS = 39 degrees

The answer is B.

Answer 2

Answer:

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

Step-by-step 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

$Inscribed angle=\frac{1}{2}Intercepted arc$            (1)

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

${\angle}UVS=\frac{1}{2}arc US$

${\angle}UVS=\frac{1}{2}(78^{\circ})$

${\angle}UVS=39^{\circ}$

Therefore, option B is correct.