Two horizontal lines are cut by a transversal. what is the least number of angle measures you need to know in order to find the measure of every angle? explain your reasoning

The answer is only one angle. Explained.

Step-by-step explanation: As given in the question and shown in the attached figure, the lines horizontal lines 'p' and 'q' are cut by the transversal 'r'. We need to determine the least number of angles among the eight angles mentioned in the figure to find the measure of all the angles.

Suppose, the measure of ∠1 is given as x°.

So, ∠2 = 180° - x (linear pair of angles),

∠3 = x (=∠1, vertically opposite angles),

∠4 = 180° - x (=∠2, verticaly opposite angles),

∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, ∠4 = ∠8. These are pairs of correspomding angles.

Thus, we need the measure of only one angle to find the measure of all the angles.

Hence explained.