Question

C

Answer 1

The arc angle AC is measured as 55 degrees.

How to find arc angle?

If two secant intersect in the exterior of a circle, then the measure of the angle formed is half the positive difference of the arcs intercepted.

Therefore, the secants intersect outside the circle at point E.

The arc angle AC can be found as follows:

Therefore,

m∠BED = 1 / 2 (arc angle AC - arc angle BD)

arc angle AC = x

arc angle BD = 23 degrees.

m∠BED = 16 degrees.

m∠BED = 1 / 2 (arc angle AC - arc angle BD)

16 = 1 / 2 (x - 23)

16 = 1 / 2x - 23 / 2

16 + 11.5 = 0.5x

27.5 = 0.5x

x = 27.5 / 0.5

x = 55 degrees.

Therefore,

arc angle AC = 55 degrees.

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