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 $90^o$. One can start the problem by assuming the angles according to the condition given then applying the above elaborated condition of complementary angles, one can easily find the angles required.

Complete step by step solution:
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,
$10x=90$
$\Rightarrow x = 9^o$

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.
This question can also be asked in another way, in which we need to find the complement or supplement of the angle given, then using the conditions of complementary and supplementary angles we can find the required values.

Additional Information:
Supplementary Angles: Two angles are said to be complementary if the sum of their measures is $180^o$.