Question 855456
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the complementary  angle  of  an   given  angle  is  2/5  th  of  the  supplementary  angle.  what  is   the  measure  of  given  angle?
Ans:
Let the angle be x.
Sum of an angle and complementary angle is 90.
Sum of an angle and supplementary angle is 180.
Complementary angle = 90 - x
Supplementary angle = 180 - x
Given that {{{90 - x = (2/5)*(180 - x)}}}
i.e.
{{{5*(90 - x) = 2*(180 - x)}}}
{{{450 - 5*x = 360 - 2*x}}}
{{{3*x = 90}}} or {{{x = 30}}}

Check: If x is 30, complementary angle = 60, supplementary angle = 150
60 is 2/5 times 150. Correct!

Hope this helps :)
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