Question

Choose the pairs of complementary angles
[a] $30{}^\circ $ and $150{}^\circ $
[b] $76{}^\circ $ and $14{}^\circ $
[c] $65{}^\circ $ and $65{}^\circ $
[d] $120{}^\circ $ and $30{}^\circ $

Answer 1

Hint: The measure of complementary angles add up to $90{}^\circ $. So, find the pairs, the sum of whose measures add up to $90{}^\circ $. Then those pairs form pairs of angles that are complementary angles.

Complete step-by-step answer:

Complementary angles: Two angles whose measures add up to $90{}^\circ $ are called complementary angles, e.g. $60{}^\circ $ and $30{}^\circ $ are complementary angles.
Supplementary angles: Two angles whose measures add up to $180{}^\circ $ are called supplementary angles, e.g. $60{}^\circ $ and $120{}^\circ $
The reflex angle of an angle: The measure of an angle and its reflex sum up to $360{}^\circ $.
[a] 30+150 = 180
Hence $30{}^\circ +150{}^\circ =180{}^\circ $
Hence the angles are supplementary.
[b] 76+14 = 90
Hence $70{}^\circ +14{}^\circ =90{}^\circ $
Hence the angles are complementary
[c] 65+65 =130
Hence $65{}^\circ +65{}^\circ =130{}^\circ $
Hence the angles are neither complementary nor supplementary
[d] 120+30 = 150
Hence $120{}^\circ +30{}^\circ =150{}^\circ $
Hence the angles are neither supplementary nor complementary.
Hence the angles $76{}^\circ $ and $14{}^\circ $ are the only angles that are complementary.
Hence option [b] is correct.

Note: [1] There is usually a confusion whether supplementary angles sum up to $180{}^\circ $ or whether complementary angles add up to $180{}^\circ $. In that case, one can memorise as follows:
In the English alphabet, s comes after c. So s>c. So, supplementary angles add up to $180{}^\circ $ , and complementary angle add up to $90{}^\circ $