Question

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

Explanation:

Step1: Recall the intersecting - chords angle formula

The measure of an angle formed by two intersecting chords in a circle is half the sum of the measures of the intercepted arcs. Let the two intercepted arcs be $a$ and $b$. The formula for the measure of the angle $\theta$ formed by the two chords is $\theta=\frac{1}{2}(a + b)$.

Step2: Identify the intercepted arcs

The intercepted arcs for $\angle1$ are the arcs with measures $37^{\circ}$ and $25^{\circ}$.

Step3: Calculate the measure of $\angle1$

Using the formula $\angle1=\frac{1}{2}(37^{\circ}+ 25^{\circ})$. First, add the arc - measures: $37^{\circ}+25^{\circ}=62^{\circ}$. Then, divide by 2: $\frac{62^{\circ}}{2}=31^{\circ}$.

Answer:

$31^{\circ}$