Question

the complement of an angle is $\frac{1}{4}$ of its supplement. Find the angle

Answer 1

$\red{\huge{ANSWER}}$

$\rm{60}$

$\mathbb{EXPLANATION}$

$\boxed{\pink{\rm{Two\:Angles\:Are\:Said\:To\:Be\: Complement}}}$

$\boxed{\pink{\rm{If\:There\:Sum\:=90}}}$

$\boxed{AND}$

$\boxed{\pink{Two\:Angles\:Are\:Said\:To\:Be\:Suppplement\:}}$

$\boxed{\pink{\rm{If\:There\:Sum\:=180}}}$

$\rm{Let\:The\:Angle\:Be\:x}$

$\underline{ACCORDING\:TO\:THE\:QUESTION}$

$\rm{\left(90-x\right)=\frac{1}{4}\left(180-x\right)}$

$\rm{\left(90-x\right)=\left(45-\frac{x}{4}\right)}$

$\rm{\left(90-45\right)=\frac{3x}{4}}$

$\rm{x=60}$

$\therefore$ $\rm{The\:Angle\:Is\:60}$

Answer 2

♡$\huge\underline\mathcal{Heyaa}$♡

Let the angle be x

Its complement = ( 90 - x)

Its supplement = ( 180 - x)

According to the question :

=> ( 90 - x) = 1/4 ( 180 - x)

=> ( 90 - x) = ( 45 - x/4 )

=> 90 - 45 = -x/4 + x

=> 90 - 45 = 3x/4

=> x = 60

Therefore, the angle is 60°

Also note :

☆ If the sum of two angles is 90°, then they are said to be complementary

☆ If the sum of two angles is 180°, then they are said to be supplementary

♡$\huge\underline\mathcal{Thanks}$♡