Question

The intersection of parallel lines b and c and transversal line d form several special angle relationships, as shown in the image below.

Which pairs of angles are congruent? Select all that apply.

angle 1 and angle 4

angle 3 and angle 5

angle 2 and angle 8

angle 3 and angle 7

Answer 1

`\angle 1 = \angle 4`

`\angle 3= \angle 7`

Explanation:

`\angle 1 = \angle 4`

Since they are vertically opposite angles

Since b || c

`\angle 3= \angle 6` --1

Since they are alternate interior angles.

`\angle 7= \angle 6` --2

Since they are vertically opposite angles

So, By 1 and 2

`\angle 3= \angle 7`

So, Option 1 and option 4 are the pairs of angles which are congruent.

Answer 2

The correct answers are

angle 1 and angle 4

angle 3 and angle 7

Explanation:

From the given figure we can see that,

b and c are parallel lines.

The correct answers are,

1). angle 1 and angle 4

Angle 1 and 4 are vertically opposite angles. Vertically opposite angles are equal.Therefore angle 1 congruent angle 4

2). angle 3 and angle 7

angle 3 and angle 7 are corresponding angles on same side which are equal. Therefore angle 3 congruent angle 7