Question

PLEASE HELP ME Given O below, if XY and YZ are congruent, what is the measure of YOZ

Answer 1

140°

Explanation:

1. full the circle is 360°;

2. YZ+XY=360-80; ⇔ YZ+XY=280;

3. if YZ=XY, then YZ=XY=280/2=140, ⇒ YOZ=140°

Answer 2

C.
`140^(\circ)`

Explanation:

We have been given an image of circle O, in which arc XY is congruent to arc YZ. We are asked to find the measure of angle YOZ.

We know that the degree measure of a circle is 360 degrees. We can see that angle YOZ is central angle, so its measure will be equal to arc YZ.

We can set an equation to find the measure of arc YZ as:

`\text{Arc YZ+ Arc XY+Arc XZ}=360^(\circ)`

`\text{Arc YZ+ Arc XY}+80^(\circ)=360^(\circ)`

`\text{Arc YZ+ Arc XY}=360^(\circ)-80^(\circ)`

`\text{Arc YZ+ Arc XY}=280^(\circ)`

`\text{2*Arc YZ}=280^(\circ)` As
`\text{Arc XY}=\text{Arc YZ}`

`\text{Arc YZ}=(280^(\circ))/(2)`

`\text{Arc YZ}=140^(\circ)`

Therefore, measure of angle YOZ is 140 degrees and option C is the correct choice.