Question

use the diagram showing m || n, as well as the relationships between interior and exterior angles of δabc, 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

Angle ABC is supplementary to 60°.
$180^\circ - 60^\circ = 120^\circ$

Step2: Find angle BAC

Angle at A: vertical angle to 70°? No, angle BAC is $180^\circ - 70^\circ - $ (angle from m)? Wait, alternate angles: since m||n, angle at A (BAC) and the angle supplementary to 70°? Wait, angle BAC is $180^\circ - 70^\circ - $ the angle at A (let's see: the angle at A opposite to q-p is equal to angle BAC? Wait, correct: angle BAC is $180^\circ - 70^\circ - 60^\circ$? No, triangle sum: angle ABC=120°, so angle BAC + angle ACB = 60°. Wait, angle BAC is equal to the angle at A: since m||n, the angle at A (between line AB and m) is equal to the angle at B (between line AB and n)? No, angle BAC is $50^\circ$? Wait, correct calculation: angle ABC = 120°, angle BAC: the angle at A is $180^\circ - 70^\circ - 60^\circ = 50^\circ$? Yes, then angle ACB = 180-120-50=10°? Wait, no: let's recheck. Angle ABC: the angle at B is 180-60=120°, correct. Angle BAC: the angle at A is 180-70-60=50° (since the straight line at A has angles summing to 180: 70 + angle BAC + 60=180 → angle BAC=50). Then angle ACB=180-120-50=10°.

Step3: Find angle ACB

Triangle sum: $180^\circ - 120^\circ - 50^\circ = 10^\circ$

Answer:

The measure of angle ABC is 120°
The measure of angle BAC is 50°
The measure of angle ACB is 10°