The problem involves a circle, two intersecting secants, and the measurement of the intercepted arcs. Given the diagram and the arc measurements, we can use a key geometric property of secants:

Formula for Secants Intersecting Outside a Circle:

When two secants intersect outside a circle, the measure of the angle formed (denoted as $x$) is half the difference between the measures of the intercepted arcs. This can be expressed as:

$x = \frac{1}{2} \left( \text{larger arc} - \text{smaller arc} \right)$

Given Values:

• Larger arc: $74.2^\circ$
• Smaller arc: $30.3^\circ$