In a circle centered at point O, the diameter AB = 16, the chord AK = 8. Find the degrees measure of the angle ABK.

Let’s finish the diameter AB and the chord AK to the triangle ABK.

Since AB is the diameter of a circle, the degree measures of arcs AB and AKB = 360/2 = 180.

The inscribed angle AKB rests on an arc of 180, then the angle AKB = 180/2 = 90, and therefore the triangle ABK is rectangular.

In a right-angled triangle SinABK = AK / AB = 8/16 = 1/2.

Then the angle ABK = arcsin (1/2) = 30.

Answer: Angle ABK is 30.

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