Question

which equation is correct regarding the measure of ∠mnp?
○ (mangle mnp=\frac{1}{2}(x - y))
○ (mangle mnp=\frac{1}{2}(x + y))
○ (mangle mnp=\frac{1}{2}(z + y))
○ (mangle mnp=\frac{1}{2}(z - y))

Explanation:

Step1: Recall the angle - measure formula for an angle formed by a tangent and a secant.

The measure of an angle formed by a tangent and a secant of a circle is half the difference of the measures of the intercepted arcs.
In the given circle, the angle $\angle MNP$ is formed by tangent $NP$ and secant $MN$. The intercepted arcs are arc $x$ and arc $y$.
The formula for the measure of $\angle MNP$ is $m\angle MNP=\frac{1}{2}(x - y)$.

Answer:

$m\angle MNP=\frac{1}{2}(x - y)$ (First option)