Question

Which of the following pairs of angles is not necessarily congruent

Answer 1

E.
`\angle 3` and
`\angle 5`.

Step-by-step explanation:

According to the figure, we have the following conclusions:

1)
`\angle 1` and
`\angle 2` are vertical opposite angles. (
`m \angle 1 = m \angle 2`)

2)
`\angle 2` and
`\angle 3` are internal alternate angles. (
`m \angle 2 = m\angle 3`)

3)
`\angle 2` and
`\angle 4` are corresponding angles. (
`m\angle 2 = m\angle 4`)

4)
`\angle 3` and
`\angle 4` are vertical opposite angles. (
`m \angle 3 = m \angle 4`)

But,
`\angle 3` and
`\angle 5`, since
`m \angle 3 + m\angle 6 + m\angle 5 = 180^(\circ)`, where
`\angle 3` is an acute angle and
`\angle 6` is a right angle, and
`m \angle 4 + m \angle 5 = 90^(\circ)`. Then,

`m\angle 5 = 90^(\circ) -m\angle 4`.

`m\angle 5 = 90^(\circ)-m\angle 3`

Hence, the right answer is E.