Question

in the figure below, ∠dcb is an exterior angle of △abc. what is the measure of ∠a? select one answer a 63° b 64° c 67° d 71°

Explanation:

Step1: Recall Exterior Angle Theorem

The exterior angle of a triangle is equal to the sum of the two non - adjacent interior angles. So, \(m\angle DCB=m\angle A + m\angle B\).

Step2: Find \(m\angle A\)

We know that \(m\angle DCB = 116^{\circ}\) and \(m\angle B=49^{\circ}\). Let \(m\angle A=x\). Then, by the exterior angle theorem, \(116^{\circ}=x + 49^{\circ}\).
To solve for \(x\), we subtract \(49^{\circ}\) from both sides of the equation: \(x=116^{\circ}- 49^{\circ}\).
Calculating \(116 - 49=67\), so \(m\angle A = 67^{\circ}\).

Answer:

C \(67^{\circ}\)