Question

the compliment of an angle is 1/4 of its supplement. find the angle​

Answer 1

SoluTion :-

Let the angle be x

Since complementary angles sum up to 90°,

The complement of the angle is 90° -  x

Since complementary angles sum up to 180°,

The supplement of the angle is 180° - x

According to the question,

$\sf {90^{o} - x = \dfrac{1}{4} \times (180^{o} - x)}\\\\\\\sf {4 (90^{o} - x)=180^{o} - x}\\\\\\\sf {360^{o} - 4x=180^{o} -x}\\\\\\\sf {360^{o} -180^{o} =3x}\\\\\\\sf {180^{o} =3x}\\\\\\{x=60^{o}}$

Thus, the angle is 60°