The sum of the supplement of angle $144^{\circ}$ and complement of angle $54^{\circ}$ is:-

Question

Accepted Answer

The correct option is 3:
To solve this problem, we need to recall the definitions of supplementary and complementary angles.

Key Concepts:1.  Supplementary Angles: Two angles are supplementary if their sum is $180^{\circ}$. If an angle is $x$, its supplement is $180^{\circ} - x$.
2.  Complementary Angles: Two angles are complementary if their sum is $90^{\circ}$. If an angle is $y$, its complement is $90^{\circ} - y$.Step-by-step explanation:

Step 1: Find the supplement of angle $144^{\circ}$.
The supplement of $144^{\circ}$ is $180^{\circ} - 144^{\circ}$.
$$180^{\circ} - 144^{\circ} = 36^{\circ}$$

Step 2: Find the complement of angle $54^{\circ}$.
The complement of $54^{\circ}$ is $90^{\circ} - 54^{\circ}$.
$$90^{\circ} - 54^{\circ} = 36^{\circ}$$

Step 3: Calculate the sum of the supplement and the complement found in Step 1 and Step 2.
Sum = (Supplement of $144^{\circ}$) + (Complement of $54^{\circ}$)
Sum = $36^{\circ} + 36^{\circ}$
$$36^{\circ} + 36^{\circ} = 72^{\circ}$$
Therefore, the sum of the supplement of angle $144^{\circ}$ and the complement of angle $54^{\circ}$ is $72^{\circ}$. This matches Option 3.

The incorrect option is 1:
$36^{\circ}$ is the value of the supplement of $144^{\circ}$ or the complement of $54^{\circ}$ individually, but not their sum.

The incorrect option is 2:
$90^{\circ}$ is an incorrect sum. This value might be chosen if one incorrectly assumes the sum of a complement and supplement or makes an arithmetic error.

The incorrect option is 4:
$180^{\circ}$ is an incorrect sum. This value might be chosen if one incorrectly assumes the sum of two supplementary angles, or if there's a misunderstanding of what is being asked to sum.