Question

An angle is one-ninth of its complementary angle. Find the angle.

Answer 1

Hint: Complementary angles: Two angles are said to be complementary if the sum of their measures is $90^o$.

Complete step-by-step answer:
Let the required angle be x.
Then, by using the condition of complementary angles, another angle is 90 – x.
Also, we are given that the required angle is one-ninth of its complementary angle. Thus,
$x=\dfrac{1}{9} \times (90-x)$
Cross multiplying, we get,
$9x=90-x$
Rearranging the terms, we get,
$10x=90$
$\implies x = 9^o$
Hence, the required angle is $9^o$.

Note: In this type of questions, we start by assuming the angles and then using the condition given we can compute the required angle.
Supplementary Angles: Two angles are said to be complementary if the sum of their measures is $180^o$.