Question

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

Explanation:

Step1: Recall exterior - angle theorem

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

Step2: Identify non - adjacent interior angles

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

Step3: Calculate the exterior angle

The measure of the exterior angle at \(M\) is \(m\angle L + m\angle N=54^{\circ}+ 24^{\circ}=78^{\circ}\)

Answer:

B. \(78^{\circ}\)