Question

in circle y, what is ( mangle 1 )?
( 6^circ )
( 25^circ )
( 31^circ )
( 37^circ )

Explanation:

Step1: Recall intersecting chords angle theorem

The measure of an angle formed by two intersecting chords is half the sum of the measures of the intercepted arcs.

Step2: Identify intercepted arcs

The intercepted arcs for $\angle 1$ are $37^\circ$ and $25^\circ$.

Step3: Calculate $m\angle 1$

$$m\angle 1 = \frac{1}{2} \times (37^\circ + 25^\circ)$$
$$m\angle 1 = \frac{1}{2} \times 62^\circ$$
$$m\angle 1 = 31^\circ$$

Answer:

31° (Option C)