Question

What is the supplement of an angle that measures 20 degrees?

Answer 1

Hint: Two angles are supplementary, if they sum up to 180${}^{\circ }$, i.e. if we have one angle $\mathrm{\angle }A$ and the other angle is $\mathrm{\angle }B$, then $\mathrm{\angle }A$ and $\mathrm{\angle }B$ are supplementary, if $\mathrm{\angle }A+\mathrm{\angle }B={180}^{\circ }$. So, to calculate the supplementary angle of any given angle, we just subtract that angle from${180}^{\circ }$. In terms of geometry, two angles which are supplements of each other lie on a straight line. Also, if two angles are supplementary, we say the first angle is “supplement” of the other, i.e. in this case $\mathrm{\angle }A$ is a “supplement” of $\mathrm{\angle }B$.

Complete step-by-step solution:
Here, we are given an angle measurement of ${20}^{\circ }$ and we need to find the supplementary angle of this measurement.
In terms of geometry, two angles which are supplements of each other lie on a straight line. Also, if two angles are supplementary, we say the first angle is “supplement” of the other, i.e. in this case $\mathrm{\angle }A$ is a “supplement” of $\mathrm{\angle }B$.
To find the supplementary angle measurement of the given angle, we can just solve it by assuming that the supplementary angle of ${20}^{\circ }$ is $x^{\circ }$, then by definition of supplementary angles, we have:
${20}^{\circ }+x^{\circ }={180}^{\circ }$
Taking ${20}^{\circ }$ to the right hand side of the equation, we have:
$x^{\circ }={180}^{\circ }-{20}^{\circ }$
$\Rightarrow x^{\circ }={160}^{\circ }$
Hence, we have found the supplementary angle of ${20}^{\circ }$ which is ${160}^{\circ }$.

Note: When we calculate the supplementary angle, do not confuse it with complementary angle and subtract it from ${90}^{\circ }$. It is a common mistake, so always read the statement of what has been asked and then do what needs to be done. Take care of calculation mistakes while subtracting. Do NOT subtract the angle ${180}^{\circ }$ from the angle. You need to subtract the given angle from ${180}^{\circ }$.
Alternate method
To solve such a type of question, we just subtract the given angle from ${180}^{\circ }$. We have the following:
${180}^{\circ }-{20}^{\circ }={160}^{\circ }$
$\Rightarrow$ Supplementary angle of ${20}^{\circ }$ is equal to ${160}^{\circ }$.