Question

In the diagram, AOC = 144 degrees, APC = 145 degree and onis the center of the circle. Find BAD.​

Answer 1

Answer: 37 degrees

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Step-by-step explanation:

Central angle AOC is 144 degrees. This means arc ABC is 144 degrees because the central angle subtends this arc.

The remaining bit of the circle is 360-144 = 216 degrees. If we placed point E somewhere on the edge of the circle, toward the bottom, then major arc AEC is 216 degrees in measure.

Notice how inscribed angle ADC subtends this 216 degree arc. So according to the inscribed angle theorem, angle ADC is half of the 216 degree arc at 216/2 = 108 degrees.

Angle APD = 180 - (angle APC) = 180 - 145 = 35 degrees

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Focus solely on triangle ADP. We have these interior angles

• A = unknown
• D = 108
• P = 35

The three interior angles must add to 180

A+D+P = 180

A+108+35 = 180

A+143 = 180

A = 180-143

A = 37 which is the measure of angle BAD.