Circle q is shown. secant l n and tangent p n intersect at point n outside of the circle. secant l n intersects the circle at point m. arc m p is y, arc l p is x, and arc m l is z.
which equation is correct regarding the measure of ∠mnp?

m∠mnp = one-half(x – y)
m∠mnp = one-half(x + y)
m∠mnp = one-half(z + y)
m∠mnp = one-half(z – y)

FIRST OPTION.

Step-by-step explanation:

By definition, the "Angle formed by a Tangent and a Secant" is:

In this case you can identify in the figure that the Intercepted Arcs are:

  and

And the Angle formed by the tangent and the secant is:

Therefore, the following equation can be used to calculate the measure of the angle ∠MNP:

This matches with the First option.

The answer is 78.706

Step-by-step explanation:

135.826-57.120(you add a zero because it's in the decimals place, and can't be seen, makes it easier for you to solve.)

135.826-57.120= 78.706

Hope this has helped, have a great day.