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In the diagram below of circle O, chords ab and cd intersect at E.

If measure of arc AC = 72° and measure of arc AEC = 58°, how many degrees are in measure of arc DB?

In the diagram below of circle O chords ab and cd intersect at E If measure of arc AC 72 and measure of arc AEC 58 how many degrees are in measure of arc DB class=

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Answer:

Correct option: 3

Step-by-step explanation:

When we have a crossing of two chords in a circle, there is a property that relates the angles in the intersection point and the arcs defined in the circle. From this property, we have that:

mAEC = (1/2) * (mAC + mBD)

Using the values of mAEC = 58° and mAC = 72°, we have that:

58 = (1/2) * (72 + mBD)

116 = 72 + mBD

mBD = 116 - 72

mBD = 44°

Correct option: 3

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