Question

Find the measure of the arc or central angle indicated. Assume that lines which appear to be diameters are actual diameters.

Answer 1

Answer: 238 degrees

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Step-by-step explanation:

Arc RTU is a semicircle of measure 180 degrees. This is because segment RU is a diameter of the circle.

Minor arcs RS, ST, and TU all combine to form arc RTU.

RS + ST + TU = RTU

x+70+52 = 180

x+122 = 180

x = 180-122

x = 58

Minor arc RS is 58 degrees in measure.

This means central angle RCS = 58 degrees, where C is the center of the circle.

Vertical angles are always congruent, which leads to central angle VCU being 58 degrees as well. This in turn leads to minor arc UV = 58.

In short, minor arc RS = minor arc UV = 58 degrees.

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So,

arc RTV = (arc RTU) + (minor arc UV)

arc RTV = (180) + (58)

arc RTV = 238 degrees