Question

$\angle AOC$ and $\angle BOC$ are the complementary angles. If $\angle AOC = {\left( {x + 12} \right)^ \circ }$ and $\angle BOC = 2{\left( {x + 6} \right)^ \circ }$, then find the value of x.

Answer 1

Hint: At first we will understand what the complementary angles are, using the definition of the complementary angles we form an equation in $\angle AOC$ and $\angle BOC$, and we have the values of $\angle AOC$ and $\angle BOC$ in terms of x that is given to us.
Now solving that equation for we will get the value of ‘x’ i.e. the required value.

Complete step-by-step answer:
Given data: $\angle AOC$ and $\angle BOC$ are the complementary angles
$\angle AOC = {\left( {x + 12} \right)^ \circ }$
$\angle BOC = 2{\left( {x + 6} \right)^ \circ }$

When the sum of two angles is ${90^ \circ }$, then the angles are known as the complementary angles. In other words, if two angles add up to form a right angle, then these angles are referred to as complementary angles.
Now, we have given that $\angle AOC$ and $\angle BOC$ are the complementary angles
Therefore, we can say that, $\angle AOC + \angle BOC = {90^ \circ }$
Substituting the values given to us that is $\angle AOC = {\left( {x + 12} \right)^ \circ }$ and $\angle BOC = 2{\left( {x + 6} \right)^ \circ }$
$ \Rightarrow {\left( {x + 12} \right)^ \circ } + 2{\left( {x + 6} \right)^ \circ } = {90^ \circ }$
On simplifying the brackets we get,
$ \Rightarrow x + {12^ \circ } + 2x + {12^ \circ } = {90^ \circ }$
On adding the like terms we get,
$ \Rightarrow 3x + {24^ \circ } = {90^ \circ }$
Subtracting both the sides by ${24^ \circ }$ we get,
$ \Rightarrow 3x = {66^ \circ }$
Dividing both sides by 3 we get,
$\therefore x = {22^ \circ }$
There the value of x is ${24^ \circ }$.

Note: Most of the students misunderstand the complementary with the supplementary and make the addition of both angles as ${180^ \circ }$ so keep it in mind that,
When the sum of two angles is ${90^ \circ }$, then the angles are known as the complementary angles.
When the sum of two angles is ${180^ \circ }$, then the angles are known as the supplementary angles.