Question

calculating the measures
use the diagram showing ( m parallel n ), as well as the
relationships between interior and exterior angles of
( \triangle abc ), to answer the questions.
the measure of angle ( abc ) is
the measure of angle ( bac ) is
the measure of angle ( acb ) is

Explanation:

Step1: Find \(\angle ABC\)

Since \(m\parallel n\), the angle adjacent to \(60^{\circ}\) and \(\angle ABC\) are supplementary. So \(\angle ABC = 180 - 60=120^{\circ}\)

Step2: Find \(\angle BAC\)

The angle adjacent to \(70^{\circ}\) and \(\angle BAC\) are supplementary. So \(\angle BAC=180 - 70 = 110^{\circ}\)

Step3: Use the angle - sum property of a triangle

In \(\triangle ABC\), we know that \(\angle ABC+\angle BAC+\angle ACB = 180^{\circ}\)
Substitute \(\angle ABC = 120^{\circ}\) and \(\angle BAC=110^{\circ}\) into the formula:
\(120 + 110+\angle ACB=180\)
\(\angle ACB=180-(120 + 110)\)
\(\angle ACB = 50^{\circ}\)

Answer:

The measure of angle \(ABC\) is \(120^{\circ}\).
The measure of angle \(BAC\) is \(110^{\circ}\).
The measure of angle \(ACB\) is \(50^{\circ}\).