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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: \( 30.3^\circ \)

###

The architect designed a building front with an arching roof based off a circle and two intersecting secants. The values of the intercepted arcs are shown. Find x and round to 1 decimal place.

Solve this geometry problem involving secants intersecting outside a circle. Learn how to apply the secant-secant angle theorem to find the angle between secants using the formula x = 1/2 (larger arc - smaller arc). Suitable for students in Grades 9-12.

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