Question

in circle o, what is m∠maj? 50° 55° 125° 250°

Explanation:

Step1: Recall the angle - arc relationship

The measure of an angle formed by two intersecting chords in a circle is half the sum of the measures of the intercepted arcs.

Step2: Identify the intercepted arcs

The intercepted arcs for $\angle MAJ$ are $\overset{\frown}{LM}$ and $\overset{\frown}{KJ}$. Given $m\overset{\frown}{LM}=80^{\circ}$ and $m\overset{\frown}{KJ} = 170^{\circ}$.

Step3: Apply the formula

The formula for the measure of the angle formed by two intersecting chords is $m\angle MAJ=\frac{1}{2}(m\overset{\frown}{LM}+m\overset{\frown}{KJ})$.
Substitute $m\overset{\frown}{LM} = 80^{\circ}$ and $m\overset{\frown}{KJ}=170^{\circ}$ into the formula:
\[m\angle MAJ=\frac{1}{2}(80 + 170)=\frac{1}{2}(250)=125^{\circ}\]

Answer:

$125^{\circ}$