In a circle with center O, diameter MN and radius OK ∠KMO = 36 °, find ∠NOK.

univerkov | May 9, 2021 | education

Consider a triangle KOM, in which OK = OM, as the radii of a circle. So the triangle KOM is isosceles. The angle K is equal to the angle M is equal to 36 °. Then the angle of the KOM in the triangle is

180 – (36 + 36) = 108 °. And the angles NOK and МОК are adjacent, and the sum of adjacent angles is 180 °.

This means that the angle NOK will be equal to 180 – 108 = 72 °.

Answer: 72 °.

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