in circle o, what is m∠maj? 50° 55° 125° 250°
in circle o, what is m∠maj? 50° 55° 125° 250°
Answer
Explanation:
Step1: Recall the inscribed - angle theorem
The measure of an inscribed angle is half the measure of its intercepted arc.
Step2: Find the measure of the intercepted arc
The arc intercepted by $\angle MAJ$ is the sum of the arcs $\overset{\frown}{LM}$ and $\overset{\frown}{KJ}$. The sum of the arcs of a circle is $360^{\circ}$. Let the arc intercepted by $\angle MAJ$ be $x$. We know one arc is $80^{\circ}$ and another is $170^{\circ}$, and the remaining arc is $x$. So $x=360-(170 + 80)=110^{\circ}$.
Step3: Calculate the measure of $\angle MAJ$
By the inscribed - angle theorem, $m\angle MAJ=\frac{1}{2}\times110^{\circ}=55^{\circ}$.
Answer:
$55^{\circ}$