Question

An angle is 5 times its supplement. Find the angle.

Answer 1

Hint: Here, we will use Supplementary angles which add up to 180 degrees. Using this theory we will make an equation and create a second equation from the relationship of these angles mentioned in the question.

Complete step-by-step answer:
Given in the question: Angle is 5 times its supplement.
Let’s start work by converting the statement into multiple equations and then solve them.
Let us assume, x and y are supplementary angles
\[ \Rightarrow x + y = {180^o}\] - Equation 1
Let x be an angle which is 5 times its supplement
\[ \Rightarrow x = 5y\]- Equation 2
But \(x + y = {180^o}\)From equation 1
\[y = {180^o} - x\] - Equation 3
 Substituting values from equation 3 in equation 2
\[ \Rightarrow x = 5\left( {{{180}^o} - x} \right)\]
 Opening brackets, and simplifying
\[ \Rightarrow x = 5*{180^o} - 5x\]
 Taking all the variables on one side and constant’s on the other for further solving.
\[ \Rightarrow 6x = 5*{180^o}\]
Dividing 6 on both sides to get x on the left side.
 \[ \Rightarrow x = \dfrac{{5*{{180}^o}}}{6}\]
Simplifying further.
 \[ \Rightarrow x = 5*{30^o}\]
\[ \Rightarrow x = {150^o}\]
Hence, \[x = {150^o}\]

Additional information:
Complementary Angles - Two Angles are Complementary when their sum is equal to 90 degrees (Making a Right Angle). It is not necessary that they should be next to each other, as long as their total is 90 degrees.
Supplementary Angles - Two Angles are Supplementary when their sum is equal to 180 degrees (Making a half cycle). It is not necessary that they should be next to each other, as long as their total is 180 degrees.

Note: In these types of questions, we proceed with the highlight of the question that is supplementary angles which makes their sum equal to 180 degrees. Same as this question we can proceed with complementary angles also which makes their sum equal to 90 degrees.