Question

The measures of some angles are given below. Write the measures of their complementary angles.

(i) ${40}^{\circ }$

(ii) ${63}^{\circ }$

(iii)${45}^{\circ }$

(iv) ${55}^{\circ }$

(v) ${20}^{\circ }$

(vi) ${90}^{\circ }$

(vii)$x^{\circ }$

Answer 1

Complementary angles:

If the sum of the two angles is ${90}^{\circ }$ then those angles are said to be Complementary angles.

example: ${35}^{\circ }$ and ${55}^{\circ }$ are Complementary angles.

Since, ${35}^{\circ }+{55}^{\circ }={90}^{\circ }$

(i)
Let the measure of the complementary angle be $a$.
$\Rightarrow {40}^{\circ }+a={90}^{\circ }$
$\Rightarrow a={50}^{\circ }$
Hence, the measure of the complement of an angle of measure ${40}^{\circ }$ is ${50}^{\circ }$
(ii)
Let the measure of the complementary angle be $a$.
${63}^{\circ }+a={90}^{\circ }$
$\Rightarrow a={27}^{\circ }$
Hence, the measure of the complement of an angle of measure ${63}^{\circ }$ is ${27}^{\circ }$
(iii)
Let the measure of the complementary angle be $a$.
$\Rightarrow {45}^{\circ }+a={90}^{\circ }$
$\Rightarrow a={45}^{\circ }$
Hence, the measure of the complement of an angle of measure ${45}^{\circ }$ is ${45}^{\circ }$.
(iv)
Let the measure of the complementary angle be $a$.
${55}^{\circ }+a={90}^{\circ }$
$\therefore a={35}^{\circ }$
Hence, the measure of the complement of an angle of measure ${55}^{\circ }$ is ${35}^{\circ }$
(v)
Let the measure of the complementary angle be $a$.
$\Rightarrow {20}^{\circ }+a={90}^{\circ }$
$\therefore a={70}^{\circ }$
Hence, the measure of the complement of an angle of measure ${20}^{\circ }$ is ${70}^{\circ }$
(vi)
Let the measure of the complementary angle be $a$.
$\Rightarrow {90}^{\circ }+a={90}^{\circ }$
$\therefore a=0^{\circ }$
Hence, the measure of the complement of an angle of measure ${90}^{\circ }$ is $0^{\circ }$
(vii)
Let the measure of the complementary angle be $a$.
$x+a={90}^{\circ }$
$\therefore a=(90-x{)}^{\circ }$
Hence, the measure of the complement of an angle of measure $x^{\circ }$ is $(90-x{)}^{\circ }$.