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To determine the measure of angle \( 1 \) in this circle, we need to apply the rule for the angle formed by two intersecting chords within a circle. The measure of an angle formed by two intersecting chords is equal to half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

In this case:
- We have the two arcs measuring \( 44^\circ \) and \( 86^\circ \).
- Thus, angle \( 1 \) is calculated as:

\[
\text{Angle 1} = \frac{44^\circ + 86^\circ}{2} = \frac{130^\circ}{2} = 65^\circ
\]

So, the measure of angle \( 1 \) is \( 65^\circ \). The correct answer is **65**.

Would you like further details, or do you have any questions?

Here are some additional related questions:
1. How do we calculate the angle for intersecting chords if one of the arc measures is unknown?
2. What is the relationship between vertical angles formed by intersecting chords in a circle?
3. How does this method differ from finding the angle for intersecting tangents or secants outside a circle?
4. What other rules apply to angles formed inside a circle?
5. How can you verify angle measures in a circle using alternative geometric properties?

**Tip:** Remember that when chords intersect inside a circle, the angle between them depends on the arcs they intercept.

Learn how to find the measure of an angle formed by intersecting chords in a circle. In this example, angle 1 is calculated by applying the formula for angles formed by two intersecting chords and the given arcs (44° and 86°). Suitable for students in Grades 9-10.

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