Question

What is the measure of ARC XY shown in the diagram below?

Answer 1

The answer is 32 degrees. APEX

Answer 2

Answer:

arc XY = 32°

Step-by-step explanation:

To find : measure of arc XY

             ∠Z = 39°

Solution :

We will use outside angles theorem

The Outside Angles Theorem: The measure of an angle formed by two secants, two tangents, or a secant and a tangent from a point outside the circle is half the difference of the measures of the intercepted arcs.

In the given figure the intercepted arcs are arc VW and arc XY

Major arc = arc VW = 110°

Minor arc = arc XY

Using theorem ,

$\angle Z = \frac{1}{2}(\widehat{VW}-\widehat{XY})$

$39^{\circ} = \frac{1}{2}(110^{\circ}-\widehat{XY})$

$39\times 2=(110^{\circ}-\widehat{XY})$

$78 =(110^{\circ}-\widehat{XY})$

$(110-78)^{\circ} = \widehat{XY}$

$32^{\circ} = \widehat{XY}$

Hence the measure of arc XY = 32°