Question

in circle y, what is m∠1? 37° 25° 6° 25° 31° 37°

Explanation:

Step1: Recall the theorem for angles formed by two chords intersecting inside a circle.

The measure of an angle formed by two intersecting chords is equal to half the sum of the measures of the intercepted arcs. So, if we let the intercepted arcs be \( 37^\circ \) and \( 25^\circ \), then the formula for \( m\angle1 \) (and also \( m\angle2 \), since vertical angles are equal) is \( m\angle1=\frac{1}{2}(37^\circ + 25^\circ) \).

Step2: Calculate the sum of the intercepted arcs.

First, add the two arc measures: \( 37^\circ+ 25^\circ = 62^\circ \).

Step3: Apply the angle - arc relationship formula.

Now, take half of that sum: \( m\angle1=\frac{1}{2}\times62^\circ = 31^\circ \).

Answer:

\( 31^\circ \) (corresponding to the option with \( 31^\circ \))