Question

Find the angle which is half of its complement?

Answer 1

Hint- In order to find the required angle, we will use the property of complementary angle which states that two angles are complementary if and only if their sum is equal to 90 degrees.

Complete step-by-step solution -
Let the angle which is half of its complement is $x$
As, we know that, if two angles are complementary then their sum must be equal to ${90^0}$
So, if $x$ is the angle then its complementary angle will be ${90^0} - x$
But it is given that the required angle is half of its complimentary, so
$x = \dfrac{{{{90}^0} - x}}{2}$
Multiply both the side by 2, we have
$2x = {90^0} - x$
Add $x$ to both the sides, we get
$3x = {90^0}$
Divide both the side by 3, we obtain
$
  x = \dfrac{{{{90}^0}}}{3} \\
  x = {30^0} \\
$
Hence, the required angle is ${30^0}.$

Note- In order to solve such problems, students must consider the given angle in an unknown variable and use the property of the angles given in the problem to form the equation. Also, students must remember the concept of complementary angle, supplementary angle and linear pair.