Question

what is ( moverarc{po} )?
( \bigcirc ) ( 128^circ )
( \bigcirc ) ( 173^circ )
( \bigcirc ) ( 192^circ )
( \bigcirc ) ( 256^circ )

Explanation:

Step1: Recall secant-secant angle formula

The measure of an angle formed by two secants outside a circle is half the difference of the measures of the intercepted arcs. The formula is:
$$m\angle N = \frac{1}{2}(m\overset{\frown}{PO} - m\overset{\frown}{MO})$$

Step2: Substitute known values

We know $m\angle N = 45^\circ$ and $m\overset{\frown}{MO} = 83^\circ$. Plug these into the formula:
$$45^\circ = \frac{1}{2}(m\overset{\frown}{PO} - 83^\circ)$$

Step3: Solve for $m\overset{\frown}{PO}$

Multiply both sides by 2:
$$90^\circ = m\overset{\frown}{PO} - 83^\circ$$
Add $83^\circ$ to both sides:
$$m\overset{\frown}{PO} = 90^\circ + 83^\circ = 173^\circ$$

Answer:

B. 173°