Question

The complementary angle ${30^ \circ }$is
$\left( a \right){\text{ 6}}{{\text{0}}^ \circ }$
$\left( b \right){\text{ 9}}{{\text{0}}^ \circ }$
$\left( c \right){\text{ 15}}{{\text{0}}^ \circ }$
$\left( d \right){\text{ None of these}}$

Answer 1

Hint:
Here in this question we just have to only find the angle whose sum will make it equal to ${90^ \circ }$. As we know the sum of the angles of complement is ${90^ \circ }$. Therefore, to find the other angle it will be ${90^ \circ }$ minus the angle.

Complete step by step solution:
 as we already know that the angle whose sum makes ${90^ \circ }$is said to be the complementary angle.
So let us assume that there are two angles named as${a^ \circ }{\text{ and }}{{\text{b}}^ \circ }$, therefore the ${a^ \circ }$will be ${30^ \circ }$and now we have to find them i.e. ${b^ \circ }$.
Therefore, according to the question, the equation will be
$ \Rightarrow {a^ \circ } + {b^ \circ } = {90^ \circ }$
On substituting the values, we get
$ \Rightarrow {30^ \circ } + {b^ \circ } = {90^ \circ }$
On solving the above equation, we get
$ \Rightarrow {b^ \circ } = {60^0}$
Therefore, the complementary angle ${30^ \circ }$ will be${60^ \circ }$.

Hence, the option $\left( a \right)$ is correct.

Additional information:
There are two types of complementary angles, adjacent and nonadjacent.
Adjacent: the points share a typical side and vertex and are "one next to the other". The correct point is isolated into 2 points that are "nearby" to one another making a couple of contiguous, reciprocal points.
Non-Adjacent: the points don't share a typical side. The hypothesis is: If two points are reciprocal to a similar point, the proportions of the points are equivalent to one another.
If two points have an absolute proportion of 180 degrees they are called advantageous points.
The hypothesis is: If two points structure a straight line, the points are strengthening. Reciprocal points supplement or complete one another while advantageous points fill in as an extra.

Note:
This question is very simple and we can easily find the angles. But the only thing is we have to be kept in mind while calculating whether we are calculating the complementary or supplementary angle. If we did this right then we can easily get the angle as per the required question.