Question

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

Answer:

∠4=∠5=∠8=58°

There are three more angles with the same measure.

∠2=∠3=∠6=∠7=122°

Four of the angles measure 122°.

Step-by-step explanation:

A pair of parallel lines is cut by a transversal. One of the angles formed measures 58°.

Please see the attachment for parallel line and traversal line.

For two parallel line and one traversal line. Total 8 angles formed.

Out of 8 one angle measured is 58°. We will discuss rest of the seven angle.

∠1=∠4=58°         (Vertically Opposite Angle)

∠4=∠5=58°        (Alternate interior angle)

∠5=∠8=58°        (Vertically Opposite Angle)

∠1+∠2=180°         (Linear Pair)

 ∠2=122°            (∠1=58°)

∠2=∠3=122°                  (Vertically Opposite Angle)

∠3=∠7=122°                  (Corresponding Angle)

∠7=∠6=122°                  (Vertically Opposite Angle)

∠1=58°    (Given)

∠4=∠5=∠8=58°

Hence, There are three more angles with the same measure.

∠2=∠3=∠6=∠7=122°

Hence, Four of the angles measure 122°.

Answer 2

I had to draw this on paper to figure it out....4 angles measure 122.....and 4 angles measure 58