Question

If lines p and q are parallel and angle 4 = 75°, write the measures of all other angles. Explain your reasoning in 2 or more sentences and include your calculations.

A) Angle 1 = 75°, Angle 2 = 105°, Angle 3 = 75°
B) Angle 1 = 75°, Angle 2 = 75°, Angle 3 = 105°
C) Angle 1 = 105°, Angle 2 = 75°, Angle 3 = 75°
D) Angle 1 = 105°, Angle 2 = 105°, Angle 3 = 75°

Answer 1

Using the properties of parallel lines and a transversal, angle 1 and angle 3 are corresponding to angle 4 and thus also measure 75°, while angle 2 is an alternate exterior angle and measures 105°, which corresponds to option C.

Step-by-step explanation:

If lines p and q are parallel and angle 4 is given as 75°, we can determine the measures of the other angles using the properties of parallel lines intersected by a transversal. Angles that are in the same position on the parallel lines are called corresponding angles, and they are equal. Therefore, angle 1 is also 75° because it corresponds to angle 4. Similarly, angle 3 is corresponding to angle 4 on the other parallel line, making it also 75°. Angle 2 is the alternate exterior angle to angle 4, and since angle 4 is 75°, angle 2 must be 180° - 75° = 105°. Thus, the correct measures for the angles are:

Angle 1 = 75°

Angle 2 = 105°

Angle 3 = 75°

This matches option C from the given choices.