We are given a circle with two secants intersecting outside the circle. We are given the measures of the intercepted arcs, $m\stackrel{\frown}{VW}=169^\circ$ and $m\stackrel{\frown}{XY}=45^\circ$. We need to find the measure of the angle formed by the secants, $m\angle XZY$.

1. Problem Description

We are given a circle with two secants intersecting outside the circle. We are given the measures of the intercepted arcs, $m\stackrel{\frown}{VW}=169^\circ$ and $m\stackrel{\frown}{XY}=45^\circ$. We need to find the measure of the angle formed by the secants, $m\angle XZY$.

2. Solution Steps

The measure of an angle formed by two secants intersecting outside a circle is half the difference of the measures of the intercepted arcs. In this case, the intercepted arcs are $\stackrel{\frown}{VW}$ and $\stackrel{\frown}{XY}$. Therefore, we have:

$m\angle XZY = \frac{1}{2} (m\stackrel{\frown}{VW} - m\stackrel{\frown}{XY})$

Substituting the given values:

$m\angle XZY = \frac{1}{2} (169^\circ - 45^\circ)$

$m\angle XZY = \frac{1}{2} (124^\circ)$

$m\angle XZY = 62^\circ$

3. Final Answer

$m\angle XZY = 62^\circ$