Question

NEED THIS DONE ASAP!! Thank you!!​

Answer 1

`\overset{\frown}{WX}= 66^(\circ)`

Explanation:

Inscribed Angle Theorem

The measure of an inscribed angle is half the measure of the intercepted arc.

First, use the Inscribed Angle Theorem to calculate the measure of arc WY.

`\displaystyle \angle WXY=(1)/(2) \overset{\frown}{WY}`

`\implies 57^(\circ)=(1)/(2) \overset{\frown}{WY}`

`\implies \overset{\frown}{WY}= 2 \cdot 57^(\circ)`

`\implies \overset{\frown}{WY}= 114^(\circ)`

Assuming XY is the diameter of the circle:

`\implies \overset{\frown}{WY}+ \overset{\frown}{WX}= 180^(\circ)`

`\implies 114^(\circ) + \overset{\frown}{WX}= 180^(\circ)`

`\implies \overset{\frown}{WX}= 180^(\circ) - 114^(\circ)`

`\implies \overset{\frown}{WX}= 66^(\circ)`