Parallel lines s and t are cut by a transversal r. Parallel lines s and t are cut by transversal r. Clockwise from top left, the angles formed with r and s are 1, 2, 3, 4; the angles formed with r and t are 5, 6, 7, 8. Which angles are corresponding angles?

When two parallel lines are crossed by another line, the angles in matching corners are called corresponding angles and they are equal in measures

∵ Lines s and t are parallel

∴ s // t

∵ Line r intersects lines s and t

∴ Line r is the transversal

∵ Corresponding angles are formed

- Look to the attached figure

∴ ∠ 1 ≅ ∠ 5 ⇒ corresponding angles

∴ ∠ 2 ≅ ∠ 6 ⇒ corresponding angles

∴ ∠ 3 ≅ ∠ 7 ⇒ corresponding angles

∴ ∠ 4 ≅ ∠ 8 ⇒ corresponding angles

The corresponding angles are:

∠ 1 and ∠ 5

∠ 2 and ∠ 6

∠ 3 and ∠ 7

∠ 4 and ∠ 8

astha8579 astha8579 · Answer 2 · 2022-01-28T07:29:03+01:00

You can use the definition of corresponding angles to find which angles are corresponding in the given case.

The corresponding angles are:

[tex]\angle 1 , \: \rm and \: \rm \angle 5\\\angle 2, \: and \: \angle 6\\\angle 3,\: and \: \angle 7\\\angle 4, \: and \: \angle 8[/tex]

What are corresponding angles?

When two parallel lines get intersected by third line, there are four- four angles made on both the lines. They are exactly replicated on each other line. Each angle on first parallel line will have its same positioned angle on second parallel lines.

See the diagram below. The first angle and the fifth angle correspond to each other on those two given parallel lines. These angles are corresponding. Its like we're finding duplicates with same positions and measurement. Since the lines are parallel, thus the corresponding angles are same too.

Which angles are corresponding in the given context?

Using the above definition, we can see that:

For first angle, the corresponding angle is the fifth angle.

Similarly, for second angle, it is sixth angle and so on.

Thus, the list of corresponding angles is

[tex]\angle 1 , \: \rm and \: \rm \angle 5\\\angle 2, \: and \: \angle 6\\\angle 3,\: and \: \angle 7\\\angle 4, \: and \: \angle 8[/tex]

See the diagram below to refer.

Learn more about corresponding angles here:

https://brainly.com/question/23134162