Question

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

Explanation:

Step1: Recall the angle - subtraction formula for angles formed by two chords.

The measure of an angle formed by two chords in a circle is half the difference of the measures of the intercepted arcs. Let the arcs intercepted by the angles be $a$ and $b$. The formula for the measure of the angle $\theta$ formed by the two chords is $\theta=\frac{1}{2}(a - b)$. Here, assume the larger arc is $37^{\circ}$ and the smaller arc is $25^{\circ}$.

Step2: Calculate the measure of $\angle1$.

$m\angle1=\frac{1}{2}(37^{\circ}- 25^{\circ})$. First, calculate the difference inside the parentheses: $37 - 25=12$. Then, divide by 2: $\frac{12}{2}=6^{\circ}$.

Answer:

$6^{\circ}$