High School

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WZ and XR are diameters of circle C.

The diagram is not drawn to scale.

- Circle C is shown.
- Radii are drawn from point C to point R (right), point Z (upper right), point Y (upper left), point X (left), and point W (lower left).
- Angle \(\angle Y C Z\) measures 112 degrees.
- Angle \(\angle X C W\) measures 63 degrees.
- Points X, C, and R are all on the horizontal diameter of the circle.

What is the measure of convex arc \(ZWX\)?

A. 355º
B. 5º
C. 292º
D. 243º

Answer :

The measure of convex arc upper Z is 243⁰ Option D

How to find the measure of the angle?

We should be aware that a convex angle is the angles that are irregular in nature

Assume that the radius of the given circle is r.

The central angle of the lower arc ZWX = 41+180 = 221⁰

Note that then central angle of the upper arc ZWX = 360- 221⁰

This implies that the central angle of the upper arc ZWX = 360-221 = 139⁰

Recall that Lenght of arc = A/360 *2*π*r

Where A is the angle made by the radii, r= radius of the circle

Arc length of upper ZWX:

Arc length of upper ZWX = 139π/180*r

Arc length of upper ZWX = 139πr/180

The lenght is (139*22)/ 180*7

= 3058/2360

= 245⁰

In conclusion the measure of the convex upper is 245⁰

Learn more about measure of angles on https://brainly.com/question/14684647

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Rewritten by : Jeany