Question

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

Answer 1

The answer is 32 degrees. APEX

Answer 2

arc XY = 32°

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 = (1)/(2)(\widehat{VW}-\widehat{XY})`

`39^(\circ) = (1)/(2)(110^(\circ)-\widehat{XY})`

`39* 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°