Question

segment nm is tangent to the circle. which equation correctly describes the relationship between arc and angle measures in the figure? m∠n = 1/2(mmq + mmp - mpq) m∠n = 1/2(mpq) m∠n = 1/2(mmq - mmp) m∠n = 1/2(mmp)

Explanation:

Step1: Recall tangent - secant angle formula

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. Here, the tangent is $NM$ and the secant is $NPQ$. The intercepted arcs are $\overset{\frown}{MQ}$ and $\overset{\frown}{MP}$.
The formula for the measure of $\angle N$ (formed by the tangent $NM$ and the secant $NPQ$) is $m\angle N=\frac{1}{2}(m\overset{\frown}{MQ}-m\overset{\frown}{MP})$.

Answer:

$m\angle N=\frac{1}{2}(m\overset{\frown}{MQ}-m\overset{\frown}{MP})$