Question

In the diagram shown, line m is parallel to line n. Cruz says that ∠4 and ∠6 are congruent angles. Is he correct? Why or why not?

Answer 1

(B)
`{\angle}4` and
`{\angle}7` are congruent corresponding angles and
`{\angle}7` and
`{\angle}6` are vertical angles.

Explanation:

It is given that line m is parallel to line n.

Now,
`{\angle}4` is congruent to
`{\angle}7` because they are corresponding angles which are always congruent.

Also,
`{\angle}7` is congruent to
`{\angle}6`, because they form vertically opposite angle pair, thus

`{\angle}4` will be congruent to
`{\angle}6`.

Hence, Cruz is correct that
`{\angle}4` is congruent to
`{\angle}6` because
`{\angle}4` and
`{\angle}7` are congruent corresponding angles and
`{\angle}7` and
`{\angle}6` are vertical angles.

Therefore, option B is correct.