Question

Find the complementary and supplementary angles of ${55^ \circ }$ and write the type of angle for the resultant one.

Answer 1

Hint: The sum of complementary angles is ${90^ \circ }$. To find the complement of angle ${55^ \circ }$ we just need to subtract it from ${90^ \circ }$ because we know that the sum of complementary angle is ${90^ \circ }$. The sum of the supplementary angle is ${180^ \circ }$. In this question to find the supplement of the given angle, we just need to subtract it from ${180^ \circ }$ because we know that the sum of supplementary angles is ${180^ \circ }$.

Complete step-by-step answer:
Two angles are complementary when their angle measures ${90^ \circ }$.
Let the $\angle 1$ be x and $\angle 2$ be ${55^ \circ }$
$\angle 1 + \angle 2 = {90^ \circ }$
\[\begin{gathered}
   \Rightarrow x + {55^ \circ } = {90^ \circ } \\
   \Rightarrow x = {90^ \circ } - {55^ \circ } = {35^ \circ } \\
\end{gathered} \]
Hence, the complement of angle ${55^ \circ }$ is \[{35^ \circ }\].
Here, \[{35^ \circ }\]< \[{90^ \circ }\] this implies that \[{35^ \circ }\]is an Acute angle.
Again Let the $\angle 1$ be x and $\angle 2$ be ${70^ \circ }$
$\angle 1 + \angle 2 = {180^ \circ }$
\[\begin{gathered}
   \Rightarrow x + {55^ \circ } = {180^ \circ } \\
   \Rightarrow x = {180^ \circ } - {55^ \circ } = {125^ \circ } \\
\end{gathered} \]
Hence, the supplement of angle ${55^ \circ }$ is \[{125^ \circ }\].
Here, \[{125^ \circ }\]> \[{90^ \circ }\] this implies that \[{125^ \circ }\] is an Obtuse angle.

Note: Two angles are called supplementary angles if their sum is 180 degrees. Two angles are supplementary: 1) When One of its angles is obtuse angle (angle more than 90 degree) and another angle is acute angle (less than 90 degree) 2) When both the angles are right angles.
Few more important things about supplementary angle:
Two acute angles can never form a supplementary angle. Acute angles measure angles greater than 0 degree and less than 90 degrees. If you add any two acute angles, its sum will always be less than 180 degrees.
Two obtuse angles can never form a supplementary angle. Obtuse angles measure angles greater than 90 degree. If you add two obtuse angles, their sum will always be greater than 180 degree.
Two right angles always form a supplementary angle.
Two angles are complementary angles if their sum is \[{90^ \circ }\]. Only two Acute angles can be complementary angles.