Question

in circle y, what is $m\angle1$?○ $6^\circ$○ $25^\circ$○ $31^\circ$○ $37^\circ$

Explanation:

Step1: Recall intersecting chords angle theorem

The measure of an angle formed by two intersecting chords inside a circle 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 $\angle 1$

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

Answer:

31° (Option C)