Question

review m1t3
the figures shown each have a set of parallel lines intersected by a transversal.
based on the figures, what are the measures of x, y, and z in degrees?
move the correct answer to each box in the table. each answer may be used more than once. not all answers will be used.
30° 50° 60° 100° 120° 150°
angle measures
unknowns value

Explanation:

Step1: Recall angle - relationships in parallel lines cut by a transversal

When parallel lines are cut by a transversal, vertical angles are equal, corresponding angles are equal, and same - side interior angles are supplementary (add up to 180°).

Step2: Analyze the figure for angle \(x\)

In the first figure, the angle marked \(x\) and the 45° angle are vertical angles. So \(x = 45^{\circ}\).

Step3: Analyze the figure for angle \(y\)

In the fourth figure, the angle adjacent to \(y\) and the 30° angle are complementary (since the right - angle is 90°). So \(y=60^{\circ}\) because \(90 - 30=60\).

Step4: Analyze the figure for angle \(z\)

In the second figure, the angle adjacent to \(z\) and the 60° angle are vertical angles. The angle adjacent to \(z\) is 60°. Since the angle formed by the right - angle and the adjacent angle to \(z\) and \(z\) itself form a straight - line (180°), \(z = 120^{\circ}\) (because \(180 - 60=120\)).

Answer:

Unknowns	Value
\(y\)	\(60^{\circ}\)
\(z\)	\(120^{\circ}\)