Question

In the accompanying diagram of (triangle) ABC, AB is extended
to D, exterior angle CBD measures 145°, and m(angle)C = 75.

What is mZ CAB?

Answer 1

Given that:

$m\angle CBD=145^{\circ},m\angle C=75^{\circ}$

Angle ABD is the sum of the angles CBD and CBA. Find angle CBA.

$\begin{gathered} m\angle ABD=m\angle CBD+m\angle CBA \\ 180^{\circ}=145^{\circ}+m\angle\text{CBA} \\ m\angle CBA=180^{\circ}-145^{\circ} \\ =35^{\circ} \end{gathered}$

Use the fact that the sum of the interior angles of a triangle is 180 degrees.

Here the sum of the interior angles of triangle ABC is 180 degrees.

$\begin{gathered} m\angle CAB+m\angle ABC+m\angle BCA=180^{\circ} \\ m\angle CAB+35^{\circ}+75^{\circ}=180^{\circ} \\ m\angle CAB+110^{\circ}=180^{\circ} \\ m\angle CAB=180^{\circ}-110^{\circ} \\ =70^{\circ} \end{gathered}$

The measure of the angle CAB is 70 degrees.

Second option is correct.