Question

A side view of the top of a building is shown in the diagram below. The measure of angle MNT is 72 degrees. The measure of angle QTS is 34 degrees. Line segment SQ is parallel to line segment MN. Find the measure of angle QSR.

Answer 1

142°

Explanation:

Make a line parallel to RT to create alternate internal angles

Answer 2

• 142°

Explanation:

Since QS ║ MN, the following equations are true:

• m∠SQT = m∠QNM as alternate interior angles
• m∠QNM = 180° - 72° = 108° as linear pair

The angle QSR is exterior of ΔSQT.

Exterior angle measure is the sum of non-adjacent interior angles:

• m∠QSR = m∠SQT + m∠STQ
• m∠QSR = 108° + 34° = 142°