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Question

Answers

A. ${36^ \circ }$

B. ${30^ \circ }$

C. ${150^ \circ }$

D. ${180^ \circ }$

Answer

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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 ${150^ \circ }$