Question

The figure shows lines r, n, and p intersecting to form angles numbered 1, 2, 3, 4, 5, and 6. All three lines lie in the same plane. Based on the figure, which of the individual statements would provide enough information to conclude that line r is perpendicular to line p? Select all that apply.

Answer 1

For the lines to be perpendicular the angle between them must be 90 degree.

So for the line r perpendicular to line r means that angle between these two line is of 90 degrees.

The angle between line r and line p are,

`\angle6`
`\angle1+\angle2`
`\angle5+\angle4`
`\angle3`

So all these are of 90 degrees as these are angle between two perpendicular line.

So

`\begin{gathered} \angle6=90^(\circ) \\ \angle1+\angle2=90^(\circ) \\ \angle3=90^(\circ) \end{gathered}`

Since angle 3 and angle 6 are equal to 90 degrees.

`\angle3=\angle6`

So opton B, C, and E are correct.