Question

If the arms of one angle are respectively parallel to the arms of another angle, then the two angles are either _______ or _______.

Answer 1

Let ∠ABC and ∠PQR be two angles such that AB || PQ and BC || QR.

Suppose PQ and BC intersect at O.

Figure 1	Figure 2

Consider figure 1.

Here,

∠ABC = ∠POC .....(1) (Corresponding angle)

∠POC = ∠PQR .....(2) (Corresponding angle)

From (1) and (2), we have

∠ABC = ∠PQR

Consider figure 2.

∠ABC + ∠QOB = 180º .....(3) (If two lines are parallel, then the pair of adjacent interior angles are supplementary)

Also, ∠QOB = ∠PQR .....(4) (Alternate angles)

From (3) and (4), we have

∠ABC + ∠PQR = 180º

If the arms of one angle are respectively parallel to the arms of another angle, then the two angles are either __equal__ or __supplementary__.