Question

Can someone help me solve for this angle?

Answer 1

The point `L` is joined with center `O`.

Now in `DeltaZOL,OZ=OL`

So `angle OLZ=angle OZL=37^@`

Now `angle ZOL=180^@-angle OLZ-angle OZL=180^@-74^@=106^@`

Answer 2

106 degrees.

Explanation:

One can draw a line from the center to the edge, creating an isosceles triangle like this:

(You know it's isosceles because two of the sides are equal to the same thing - the radius of the circle.)
Because it's isosceles, you know that the two angles not formed by the radii are equal.

Knowing that the angles in a triangle sum up to 180 degrees, you can calculate the final angle with the formula (180-(37+37)), which gives you a final result of 106 degrees.