Question

NEED THIS DONE ASAP!! Thank you!!​

Answer 1

Answer:

$\overset{\frown}{WX}= 66^{\circ}$

Step-by-step 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.

  $\displaystyle \angle WXY=\dfrac{1}{2} \overset{\frown}{WY}$

$\implies 57^{\circ}=\dfrac{1}{2} \overset{\frown}{WY}$

$\implies \overset{\frown}{WY}= 2 \cdot 57^{\circ}$

$\implies \overset{\frown}{WY}= 114^{\circ}$

Assuming XY is the diameter of the circle:

$\implies \overset{\frown}{WY}+ \overset{\frown}{WX}= 180^{\circ}$

$\implies 114^{\circ} + \overset{\frown}{WX}= 180^{\circ}$

$\implies \overset{\frown}{WX}= 180^{\circ} - 114^{\circ}$

$\implies \overset{\frown}{WX}= 66^{\circ}$