WZ and XR are diameters of circle C. The diagram is not drawn to scale. (1 point)
Z
97°
X
41°
R
W
What is the measure of ZWX?
318°
277°
221°
42°
We know that WZ and XR are diameters, which means they intersect at the center of the circle. Let's call that point O.
Using the angle measures given, we can find that angle WXR is:
WXR = 180° - 97° - 41° = 42°
Now we have a triangle with angles of 41°, 42°, and 97°. We want to find the measure of angle ZOX (which we'll call y), since that will give us the measure of ZWX (which is just 2y).
Using the fact that the angles in a triangle add up to 180°, we know:
y + 97° + 42° = 180°
Simplifying:
y = 41°
So ZOX is 41°, and ZWX is twice that:
ZWX = 2(41°) = 82°
Therefore, the answer is not shown as an option but the closest one is 221°.
To find the measure of angle ZWX, we need to use the properties of angles in a circle.
Since WZ is a diameter of circle C, angle ZWX is an inscribed angle, and its measure is equal to half the measure of the intercepted arc. Similarly, since XR is also a diameter, angle ZXR is also equal to half the measure of the intercepted arc.
From the given information, we know that angle Z = 97° and angle X = 41°.
To find the measure of angle ZWX, we need to find the measure of the intercepted arc, which is the sum of the measures of arcs ZW and WX.
Since angles Z and X are inscribed angles, the angles they intercept are equal to their measures.
Arc ZW = 2 * angle Z = 2 * 97° = 194°
Arc WX = 2 * angle X = 2 * 41° = 82°
Therefore, the intercepted arc ZW + WX = 194° + 82° = 276°.
Since angle ZWX is equal to half the measure of the intercepted arc, angle ZWX = 276° / 2 = 138°.
Therefore, the measure of angle ZWX is 138°.
None of the given options match the correct answer.