What’s the angle it’s looking for ?

Given:

m(ar KN) = 2x + 151

m(ar LN) = 61°

m∠NMK = 2x + 45

To find:

m∠NMK

Solution:

By property of circle:

If a tangent and a secant intersect outside a circle, then the measure of the angle formed is one-half the positive difference of the measures of the intercepted arcs.

Multiply by 2 on both sides, we get

Subtract 90 from both sides.

Subtract 2x from both sides.

Substitute x= 0 in m∠NMK.

m∠NMK = 2x + 45

              = 2(0) + 45

              = 45

Therefore m∠NMK = 45.