Question

What is the measure of arc xy

A. 46 degrees
B. 42 degrees
C. 38 degrees
D. 40 degrees

please explain!!!!

Answer 1

The measure of XY is 46.

Answer 2

A.
`46^(\circ)`

Explanation:

We have been given an image of a circle and we are asked to find the measure of arc XY.

We will use intersecting secants theorem to solve our given problem, which states that measure of an angle formed inside a circle by two intersecting secants is half the sum of intercepted arcs.

So we can set an equation to find the measure of arc XY as:

`42^(\circ)=(1)/(2)\text{(Arc XY+Arc UV)}`

`42^(\circ)=(1)/(2)\text{(Arc XY}+38^(\circ))}`

`2*42^(\circ)=2*(1)/(2)\text{(Arc XY}+38^(\circ))}`

`84^(\circ)=\text{(Arc XY}+38^(\circ))}`

`84^(\circ)-38^(\circ)=\text{Arc XY}+38^(\circ)-38^(\circ)`

`46^(\circ)=\text{Arc XY}`

Therefore, measure of arc XY will be 46 degrees as well and option A is the correct choice.