Question

Choose the pair of complementary angles.
\[
  A.{\text{ }}30^\circ ,150^\circ \\
  B.{\text{ }}76^\circ ,14^\circ \\
  C.{\text{ }}65^\circ ,65^\circ \\
  D.{\text{ }}120^\circ ,30^\circ \\
\]

Answer 1

Hint: We had to only find that pair of angles whose sum is equal to \[90^\circ \], because the sum of two complementary angles is equal to \[90^\circ \].

Complete Step-by-Step solution:
As we know that complementary angles are those whose sum is equal to \[90^\circ \].
Like if \[a^\circ \] and \[b^\circ \] are two complementary angles then \[a^\circ + b^\circ = 90^\circ \]

And supplementary angles are those whose sum is equal to \[180^\circ \].
Like if \[a^\circ \] and \[b^\circ \] are two supplementary angles then \[a^\circ + b^\circ = 180^\circ \].

So, we are given some options and asked to find which of the following pairs is complementary.
So, let us check them one by one.
Option A. \[30^\circ + 150^\circ = 180^\circ \] So, this \[30^\circ ,150^\circ \] is the pair of supplementary angles.
Option B. \[76^\circ + 14^\circ = 90^\circ \] So, this \[76^\circ ,14^\circ \] is the pair of complementary angles.
Option C. \[65^\circ + 65^\circ = 130^\circ \] So, this \[65^\circ ,65^\circ \] is neither a pair of complementary angles nor the pair of supplementary angles.
Option A. \[120^\circ + 30^\circ = 150^\circ \] So, this \[120^\circ ,30^\circ \] is neither the pair of complementary angles nor the pair of supplementary angles.
So, the pair of complementary angles will be \[76^\circ ,14^\circ \].
Hence, the correct option will be B.

Note: Whenever we come up with this type of problem then we should remember that sum of two complementary angles in degrees is \[90^\circ \] and in radians it is \[\dfrac{\pi }{2}\], while the sum of two supplementary angles in degrees is \[180^\circ \] and in radians it is \[\pi \]. So, if we are asked to find the pair of complementary or supplementary angles then we find the sum of angles of each pair. This will be the easiest and efficient way to find the solution of the problem.