Question

the measure of angle abc is
the measure of angle bac is
the measure of angle acb is

Explanation:

Step1: Find angle ABC

Since the two lines are parallel, angle ABC is an alternate - interior angle. So, angle \(ABC = 60^{\circ}\)

Step2: Find angle BAC

The vertical angle of \(70^{\circ}\) is \(70^{\circ}\). Then, angle \(BAC=180^{\circ}-70^{\circ}=110^{\circ}\) (linear pair)

Step3: Find angle ACB

Using the triangle - angle sum theorem (\(A + B + C=180^{\circ}\) in \(\triangle ABC\)). Let \(A = 110^{\circ}\), \(B = 60^{\circ}\). Then \(C=180-(110 + 60)=10^{\circ}\)

Answer:

The measure of angle \(ABC\) is \(60^{\circ}\).
The measure of angle \(BAC\) is \(110^{\circ}\).
The measure of angle \(ACB\) is \(10^{\circ}\).