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°.