Question

Select all the correct answers.

A pair of parallel lines is cut by a transversal. One of the angles formed measures 58°. Which statements about the other seven angles formed are true?
There are three more angles with the same measure.
All the other angles have the same measure.
The rest of the angles measure 122°.
Only three of the angles measure 122°.
Four of the angles measure 122°.

Answer 1

There are three more angles with the same measure. A pair of corresponding angles and a pair of vertical angles.

Step-by-step explanation:

Answer 2

3 Answers:

• A) There are three more angles with the same measure.
• C) The rest of the angles measure 122°.
• E) Four of the angles measure 122°.

==========================================================

Step-by-step explanation:

I recommend drawing out a diagram as shown below. Angle 1 is 58 degrees.

Angle 3 is also 58 since the two angles are congruent vertical angles.

Angle 5 is equal to angle 1 due to them being corresponding angles (this only works if the lines are parallel)

Angle 8 is congruent to angle 5, for similar reasonings with angle 3 above.

So that means we have three additional angles that are 58 degrees: angle 3, angle 5, angle 8

-------------------

The rest of the angles are 122 as the diagram shows. We have four angles that make up the rest of the angles. Angle 2 and angle 1 add to 180, so

x+y = 180

58+y = 180

y = 180-58

y = 122

And you'll find the other unknown angles fit this pattern as well. Or you could use corresponding angles and vertical angles to fill out the rest of the diagram.