Question

If angle 1 is 110°, what would the other angle measures have to be in order for m || n and all p?

a. Angle 2 = 70°, Angle 3 = 110°, Angle 4 = 70°
b. Angle 2 = 110°, Angle 3 = 70°, Angle 4 = 110°
c. Angle 2 = 80°, Angle 3 = 80°, Angle 4 = 80°
d. Angle 2 = 60°, Angle 3 = 60°, Angle 4 = 60°

Answer 1

The correct answer is Angle 2 = 70°, Angle 3 = 110°, Angle 4 = 70°. This is determined by using properties of angles formed by parallel lines cut by a transversal and adjacent angles around a point. Correct option (a) Angle 2 = 70°, Angle 3 = 110°, Angle 4 = 70°,

Step-by-step explanation:

To solve for the other angle measures to ensure that lines m and n are parallel and all angles p are equal, we need to consider properties of parallel lines cut by a transversal and the angles formed around a point. Given angle 1 is 110°, we can deduce the following:

• Angle 2 must be supplementary to angle 1 (they form a linear pair), hence angle 2 must be 180° - 110° = 70°.
• Angle 3, being alternate interior with angle 1, must be equal to angle 1, and thus angle 3 is 110°.
• Angle 4, being vertical with angle 2, must be equal to angle 2, so angle 4 is 70°.

Therefore, the correct answer would be: Angle 2 = 70°, Angle 3 = 110°, Angle 4 = 70°, which corresponds to option (a).