Question

The measure of an angle which is five times its supplement is:
A. $ {36^ \circ } $
B. $ {30^ \circ } $
C. $ {150^ \circ } $
D. $ {180^ \circ } $

Answer 1

Hint: In this question, we came across supplementary angles, here, we will assume two angles whose sum would be 180 degrees because they are supplementary angles. Let’s see how to approach this question further.

Complete step-by-step answer:
According to the question we know that the measure of an angle is equal to 5 times its supplement angle.
Let x be the angle and its supplement are y.
So, we have:
 x + y = $ {180^ \circ } $ ……... ( 1)
As from the question we know that x is the 5 times its supplement therefore x = 5y.
Now, substituting the value of x in the equation 1 we get:
 $ \Rightarrow $ 5y + y = $ {180^ \circ } $
 $ \Rightarrow $ 6y = $ {180^ \circ } $
 $ \Rightarrow $ y = $ \dfrac{{{{180}^ \circ }}}{6} $
 $ \Rightarrow $ y = $ {30^ \circ } $
Now, substituting the value of y in the equation (1) we get;
x + y $ 180^\circ $
 $ \Rightarrow $ x + $ {30^ \circ } $ = $ {180^ \circ } $
 $ \Rightarrow $ x = $ {180^ \circ } $ - $ {30^ \circ } $
 $ \Rightarrow $ x = $ {150^ \circ } $
Therefore, angle which is 5 times its supplement is $ {150^ \circ } $

So, the correct answer is “Option C”.

Note: Supplementary angle which means ‘’Two angles are called supplementary angles if the sum of their degree measurements equals 180 degrees (straight line). Two angles are supplementary, if 1) both the angles measure $ 90^\circ $ that is right angles. 2) One of the angles is an acute angle (angle measures less than $ 90^\circ $ ) and another angle is an obtuse angle (angle measures more than $ 90^\circ $ but less than 180 $ ^\circ $ ).
The two angles do not need to be together or adjacent. They just need to add up to 180 degrees. If the two supplementary angles are adjacent then they will form a straight line.