in the diagram of circle a, what is m∠lmn? 90° 75° 135° 120°

Question

Accepted Answer

# Explanation:
## Step1: Find the measure of the central angle corresponding to the arc not $270^{\circ}$
The total degrees in a circle is $360^{\circ}$. If one arc is $270^{\circ}$, then the other arc $ \overset{\frown}{LN}$ (the minor arc) has measure $360^{\circ}- 270^{\circ}=90^{\circ}$

## Step2: Use the formula for the measure of an angle formed by two tangents
The measure of an angle formed by two tangents outside a circle is given by $m\angle LMN=\frac{1}{2}(m\overset{\frown}{major\ arc}-m\overset{\frown}{minor\ arc})$

We know $m\overset{\frown}{major\ arc} = 270^{\circ}$ and $m\overset{\frown}{minor\ arc}=90^{\circ}$

Substitute into the formula: $m\angle LMN=\frac{1}{2}(270^{\circ}-90^{\circ})$

$$
\begin{align*}
m\angle LMN&=\frac{1}{2}(180^{\circ})\
m\angle LMN& = 90^{\circ}
\end{align*}
$$

# Answer:
$90^{\circ}$

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Question

Explanation:

Step1: Find the measure of the central angle corresponding to the arc not \(270^{\circ}\)

Step2: Use the formula for the measure of an angle formed by two tangents

Answer: