Question
In the circle shown below, segment YZ is a diameter and parallel to chord WX. Arc WX = 50
°
.
image
What is the measure of arc XZ?
A.
25
°
B.
50
°
C.
65
°
D.
130
°
°
.
image
What is the measure of arc XZ?
A.
25
°
B.
50
°
C.
65
°
D.
130
°
Answers
GPT-4o mini
In a circle, the measure of an arc is related to the angles subtended by segments of the circle. Since segment YZ is a diameter, and WX is a chord parallel to the diameter, it helps to know that angles formed by chords parallel to the diameter are such that they subtend the same arc on either side.
Since WX intercepts arc YZ, the other arc created between points X and Z can be calculated. In a circle, the sum of the measure of arcs around a circle is 360°.
Given:
- Arc WX = 50°
The remaining arc of the circle from X to Z would be 180° (half the circle, since YZ is a diameter) minus the measure of arc WX.
Therefore, the measure of arc XZ can be calculated as follows:
\[
\text{Measure of arc XZ} = 180° - 50° = 130°
\]
Thus, the measure of arc XZ is:
**D. 130°**
Since WX intercepts arc YZ, the other arc created between points X and Z can be calculated. In a circle, the sum of the measure of arcs around a circle is 360°.
Given:
- Arc WX = 50°
The remaining arc of the circle from X to Z would be 180° (half the circle, since YZ is a diameter) minus the measure of arc WX.
Therefore, the measure of arc XZ can be calculated as follows:
\[
\text{Measure of arc XZ} = 180° - 50° = 130°
\]
Thus, the measure of arc XZ is:
**D. 130°**