Question

in △lmn, m∠l = 54° and m∠m = 24°. what is the measure of the exterior angle at n?
a. 126°
b. 78°
c. 30°
d. 102°

Explanation:

Step1: Recall exterior - angle theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles.

Step2: Identify non - adjacent interior angles

The non - adjacent interior angles to the exterior angle at $N$ in $\triangle LMN$ are $\angle L$ and $\angle M$. Given $m\angle L = 54^{\circ}$ and $m\angle M=24^{\circ}$.

Step3: Calculate the exterior angle

$m(\text{exterior angle at }N)=m\angle L + m\angle M$.
$m(\text{exterior angle at }N)=54^{\circ}+24^{\circ}=78^{\circ}$.

Answer:

B. $78^{\circ}$