L, m and n are points on the circumference of a circle with a center o. if ∠mln = 44°, find ∠mon?

m∠MON = 88°

Step-by-step 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°