Question

Determine the minimum number of angle measures you would have to know to find the measures of all the angles formed by two parallel lines cut by a transversal. Explain.

Answer 1

Measure of one angle is required.

Explanation:

Kindly refer to the image attached.

AM and BN are the two parallel lines cut by a transversal PQ.

The angles formed are:

`\angle 1, \angle 2, \angle 3, \angle 4, \angle 5, \angle 6, \angle 7 \ and\ \angle 8`.

Let, only one of the angles is known to us.

Let, it is given that
`\angle 2 = 60^\circ`

AM is a straight line, therefore

`\angle 1+\angle 2 =180^\circ\\\Rightarrow \angle 1 =180-60=120^\circ`

`\angle 1` and
`\angle 3` are vertically opposite angles, therefore must be equal to each other.

`\angle 1 = \angle 3 = 120^\circ`

`\angle 2` and
`\angle 4` are vertically opposite angles, therefore must be equal to each other.

`\angle 2 = \angle 4 = 60^\circ`

By Corresponding angle postulate, we can see the following:

`\angle 2=\angle 5 =60^\circ\\\angle 3=\angle 6 =120^\circ\\\angle 1=\angle 8 =120^\circ\\\angle 4=\angle 7 =60^\circ`

Therefore, by knowing just one angle, all the angles can be found.