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

Explanation:

Step1: Recall angle - measure formula

The measure of an angle formed by two chords intersecting inside a circle is half the sum of the measures of the intercepted arcs. Let the arcs intercepted by the angle $\angle1$ be $a$ and $b$. Here, $a = 37^{\circ}$ and $b=25^{\circ}$.

Step2: Apply the formula

The formula for the measure of the angle $\angle1$ formed by two chords intersecting inside a circle is $m\angle1=\frac{1}{2}(a + b)$. Substitute $a = 37^{\circ}$ and $b = 25^{\circ}$ into the formula: $m\angle1=\frac{1}{2}(37^{\circ}+25^{\circ})$.

Step3: Calculate the value

First, find the sum inside the parentheses: $37^{\circ}+25^{\circ}=62^{\circ}$. Then, divide by 2: $\frac{62^{\circ}}{2}=31^{\circ}$.

Answer:

$31^{\circ}$