Question

Find the complement of each of the following angles.
(i) 58°
(ii) 16°
(iii) $\frac{2}{3}$ of a right angle
(iv) 46°30'
(v) 52°43'20"
(vi) 68°35'45"

Answer 1

(i) Complement of $58°=\left(90-58\right)°$
$=32°$

(ii) Complement of $16°=\left(90-16\right)°$
$=74°$

(iii) $\frac{2}{3}\text{of a right angle}\Rightarrow \left(90\times \frac{2}{3}\right)°=60°$
$\text{Complement of}\frac{2}{3}\text{of a right angle}=\left(90-60\right)°$
$=30°$

(iv) We know that $90°=89°60\text{'}$
Complement of $46°30\text{'}=\left(89°60\text{'}-46°30\text{'}\right)°$
$=43°30\text{'}$

(v) We know that $90°=89°59\text{'}60\text{'}\text{'}$
Complement of $52°43\text{'}20\text{'}\text{'}=\left[\left(89°59\text{'}60\text{'}\text{'}\right)-\left(52°43\text{'}20\text{'}\text{'}\right)\right]$

Deg	Min	Sec
89	59	60
52	43	20
37	16	40

Hence, the measure of the angle$=37°16\text{'}40\text{'}\text{'}$.

(vi) We know that $90°=89°59\text{'}60\text{'}\text{'}$
Complement of $68°35\text{'}45\text{'}\text{'}=\left[\left(89°59\text{'}60\text{'}\text{'}\right)-\left(68°35\text{'}45\text{'}\text{'}\right)\right]$

Deg	Min	Sec
89	59	60
68	35	45
21	24	15

Hence, the measure of the required angle $=21°24\text{'}15\text{'}\text{'}$.