Question

The measure of an angle which is 5 times its supplement is
A ${30^ \circ} $
B ${60^ \circ} $
C ${120^ \circ} $
D ${150^ \circ} $

Answer 1

Hint: In this question, we have been given that we need to find out the angle which is 5 times its supplement. So firstly, we know the supplement means the sum of the angle is ${180^ \circ} $. So, to solve this question we will let the angle be any variable let suppose we take the angle equals to x. Then we have given that 5 times this angle is equal to its supplement that is ${180^ \circ} $. So accordingly, we will form the equation by adding the two angles which are x and $5x$ solve it further.

Complete step-by-step solution:
We have been provided that 5 times an angle is equal to its supplement.
So, we will let that the angle is equal to any variable let suppose x.
Now according to the question, we have been given that 5 times this angle is equal to its supplement.
5 times this angle would be equal to $5x$.
Now in the next step, we will form an equation as this 5 times this angle is equal to its supplement that is ${180^ \circ} $.

So, the equation would be $x + 5x = {180^ \circ} $.
Now we will be solving the equation further,
Now the equation will be: $6x = {180^ \circ} $.
Now we will solve the equation by separating the constant and variable,
So, the simplified equation is $x = \dfrac {{{{180} ^ \circ}}} {6} $.
From this simplified equation we can find the value of x,
So, the value of x comes out to be ${30^ \circ} $
So, we can conclude that as $x = {30^ \circ} $ therefore, option (a) is correct.

Note: In this question, we have been provided with 4 options so after forming the equation we can solve this question by another manner by keeping the values one by one but this could be hectic and the possibilities of mistakes increases so be cautious while solving it by that manner and if possible try not to solve this question by that method.