Question

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

Answer 1

The measure of the Central Angle indicated is; 45°

How to find the central angle of a circle?

The central angle will be the angle subtended at the center by arc FE and arc CB.

Now, we see that angle ∠FOB = 135° and since we know that sum of angles on a straight line is 180°, then we can say that;

Central Angle = 180° - 135° = 45°

Angle subtended by Arc CD at the center is;

θ = 180 - (81 + 45)

θ = 54°

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