Question

L, M and N are points on the circumference of a circle with a center O. If ∠MLN = 44°, find ∠MON?

Answer 1

88 degrees, using the central angle and inscribed angle theorems, the central angle, in this case MON, equals the central arc. The inscribed angle is half of the arc, in this case the central arc. So MLN is half of MON.

Answer 2

m∠MON = 88°

Explanation:

For better understanding of the solution, see the attached figure of the problem :

Given : A circle centered at O. L, M and N are the points on the circumference of the circle. m∠MLN = 44°

To Find : m∠MON

Solution : ∠MON is the angle subtended by arc MN at the center

Also, ∠MLN is subtended by the arc MN at the circumference of the circle.

Now, By using the theorem : The angle subtended by an arc at the center of a circle is twice the angle subtended by the same arc at the circle circumference.

We get, m∠MON = 2 × m∠MLN

⇒ m∠MON = 2 × 44°

⇒ m∠MON = 88°