WZ and XR are diameters of circle C. The figure is not drawn to scale.
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What is the measure of ZWX?
a. 204°
b. 278°
c. 58°
d. 302°
Since WZ and XR are diameters, they divide circle C into four quarters. Angle ZWX is an angle in one of these quarters.
We know that the sum of angles in a quarter of a circle is 90 degrees (since the sum of angles in a full circle is 360 degrees). We also know that angle ZWY is a right angle (since it is part of a diameter).
Therefore, angle ZWX is 90 degrees minus the measure of angle ZWY. Angle ZWY is 128 degrees (half of 256 degrees, since it is part of a diameter). Subtracting 128 from 90 gives us 62 degrees.
So the measure of angle ZWX is 62 degrees, which means the answer is c. 58°.
To find the measure of angle ZWX, we need to consider the properties of a circle.
1. In a circle, the measure of an angle at the center is twice the measure of the angle at the circumference that intercepts the same arc.
Since WZ and XR are diameters of the circle, angle ZWX and angle XRW are angles at the circumference that intercept the same arc.
2. A diameter of a circle forms a right angle with any tangent to the circle at its endpoint.
Since WZ and XR are diameters, we can conclude that angle WXZ and angle XWZ are right angles.
Now, let's apply these properties to find the measure of ZWX:
1. As mentioned earlier, angle ZWX and angle XRW are angles at the circumference that intercept the same arc. Since angle XRW is a right angle, angle ZWX must be half of that, which is 90°.
2. We also know that angle WXZ is a right angle.
Therefore, angle ZWX can be calculated by subtracting angle WXZ from angle ZWX:
Angle ZWX - Angle WXZ = 90° - 90° = 0°
So, the measure of ZWX is 0°.
None of the options given match this answer. Therefore, there might be an error in the question or the options provided.