1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

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

Open in App
Solution

## 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__.

Suggest Corrections
2
Join BYJU'S Learning Program
Related Videos
Vertically Opposite Angles
MATHEMATICS
Watch in App
Join BYJU'S Learning Program