Applying the angle of intersecting secants theorem, the measure of angle B is: 35°.
What is the Angle of Intersecting Secants Theorem?
The measure of the angle formed outside a circle by two intersecting secants is equal to half the positive difference of the measures of the arcs they intercept based on the angle of intersecting secants theorem.
Applying the angle of intersecting secants theorem, we have the following:
Let the missing measure of the arc for angle A be x. Therefore:
6 = 1/2(x - 17)
2(6) = x - 17
12 = x - 17
12 + 17 = x
x = 29°
m∠B = 1/2(99 - x)
Plug in the value of x
m∠B = 1/2(99 - 29)
m∠B = 35°
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