Question

If the arms of one angle are respectively parallel to the arms of another angle, then the two angles are :

• A. Neither equal nor supplementary
• B. Not equal but supplementary
• C. Equal but not supplementary
• D. Either equal or supplementary.

Answer 1

The correct option is D

Either equal or supplementary.

Let the two angles be $\angle ABC$ and $\angle PQR$.
There are two possible cases:

i)

Here,
$\angle 1=\angle 2$ [Correspoding angles] and
$\angle 2=\angle 3$ [Corresponding angles]
$\therefore \angle 1=\angle 3$
$\Rightarrow \angle ABC=\angle PQR$

ii)

Here $\angle 1+\angle 2={180}^{\circ }$ [Co-interior angles] and
$\angle 2=\angle 3$ [Corresponding angles]
$\therefore \angle 1+\angle 3={180}^{\circ }$
$\Rightarrow \angle ABC+\angle PQR={180}^{\circ }$
Hence it can be seen that the angles could either be equal or supplementary.