in circle o, what is ( mangle maj )?

Question

Accepted Answer

# Explanation:
## Step1: Find the measure of the arc opposite to ∠MAJ
The sum of the measures of the arcs of a circle is $360^{\circ}$.
Let the arc opposite to $\angle MAJ$ be arc $LKJ$.
The measure of arc $LKJ=360-(170 + 80)=110^{\circ}$

## Step2: Use the vertical - angles and inscribed - angle - formed - by - two - chords theorem
The measure of an angle formed by two chords intersecting at a point inside the circle is $\frac{1}{2}$ the sum of the measures of the intercepted arcs.
$\angle MAJ=\frac{1}{2}(170 + 80)$

## Step3: Calculate the value of $\angle MAJ$
$$
\begin{align*}
\angle MAJ&=\frac{1}{2}(170 + 80)\
&=\frac{1}{2}\times250\
& = 125^{\circ}
\end{align*}
$$

# Answer:
$125^{\circ}$

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QUESTION IMAGE

Question

Explanation:

Step1: Find the measure of the arc opposite to ∠MAJ

Step2: Use the vertical - angles and inscribed - angle - formed - by - two - chords theorem

Step3: Calculate the value of \(\angle MAJ\)

Answer: