Question

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

Hint: Before attempting this question, one should have prior knowledge about the supplementary angles and also remember to take x and y as the supplement angles and x = 5y, using the given information will help you to approach the solution of the question.

According to the given information, we know that the measures of an angle is equal to 5 times to its supplement angle
Let x and y be the supplementary angles
Which means x + y = ${180^ \circ }$ taking this as equation 1
As we know that x is the 5 times its supplement therefore
x = 5y
substituting the value of x in the equation 1 we get
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 + ${30^ \circ }$ = ${180^ \circ }$
$\Rightarrow$ 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 D”.

Note: In the above solution we came across the term “supplementary angle” which can be explained as only two angles whose sum is equal to ${180^ \circ }$ when they exist on the same side of a straight line, in supplementary angle, there are many possibilities for 2 angles to be supplementary as one angle can be acute (smaller than ${90^ \circ }$) and other is the obtuse angle (greater than ${90^ \circ }$) or both angles can be right angles which means the angle is equal to ${90^ \circ }$.