Question

what is mpo? 128° 173° 192° 256°

Explanation:

Step1: Recall the secant - secant angle formula

The measure of an angle formed by two secants intersecting outside a circle is given by $\frac{1}{2}(m\overparen{PO}-m\overparen{PM})$, where $\angle MNO$ is the angle formed by the two secants and $m\overparen{PO}$ and $m\overparen{PM}$ are the intercepted arcs. Let $m\overparen{PO}=x$ and $m\overparen{PM} = y$. We know that $\angle MNO = 45^{\circ}$ and assume the central - angle corresponding to the non - intercepted part of the circle related to the secants is $83^{\circ}$, so $y=83^{\circ}$. The formula for the angle formed by two secants $\angle MNO=\frac{1}{2}(x - y)$.

Step2: Substitute the known values into the formula

We have $45=\frac{1}{2}(x - 83)$.
Multiply both sides of the equation by 2: $45\times2=x - 83$.
So, $90=x - 83$.

Step3: Solve for $x$ (which is $m\overparen{PO}$)

Add 83 to both sides of the equation: $x=90 + 83=173^{\circ}$.

Answer:

$173^{\circ}$