Question

How many degrees are there in an angle which equals one fifth of its supplement?

Answer 1

Hint: Two Angles are Supplementary when they add up to \[{180^ \circ }\]. The two angles (\[{140^ \circ }\]and \[{40^ \circ }\]) are Supplementary Angles, because they add up to \[{180^ \circ }\]. Notice that together they make a straight angle. When the sum of two angles is \[{180^ \circ }\], then the angles are known as supplementary angles. In other words, if two angles add up, to form a straight angle, then those angles are referred to as supplementary angles. These two angles form a linear angle, where if one angle is x, then the other the angle is \[\left( {180 - x} \right)\].

Complete step by step solution: In geometry, there are many types of angles with many different measures. Some angles are related to other angles because of how their measures are related. This is the case with supplementary angles, and we have a nice rule to help us understand the definition of the supplement of an angle.The supplement of an angle, is another angle, such that the sum of the measure of first angle and the measure of second angle is equal to \[{180^ \circ }\]
Let the angle be \[x\]
Therefore, its supplementary angle would be \[\left( {180 - x} \right)\]
According to the question,
\[x = \dfrac{1}{5}{\text{ }} \times \left( {180 - x} \right)\]
After Cross multiplying, we get
\[6x = 180\]
Divide both sides by \[6\], we get
\[\begin{gathered}
  x = \dfrac{{180}}{6} \\
  x = 30 \\
\end{gathered} \]
 Therefore, the angle will be \[{30^ \circ }\]. So the answer of this question will be \[{30^ \circ }\]

Note:When the two angles add to \[{180^ \circ }\], we say they "Supplement" each other. Supplement comes from Latin supplier, to complete or "supply" what is needed