Question

Find the supplement of each of the following angles.
(i) 63°
(ii) 138°
(iii) $\frac{3}{5}$ of a right angle
(iv) 75°36'
(v) 124°20'40"
(vi) 108°48'32"

Answer 1

(i) Supplement of $63°=\left(180-63\right)°$
$=117°$

(ii) Supplement of $138°=\left(180-138\right)°$
$=42°$

(iii) $\frac{3}{5}\text{of a right angle}\Rightarrow \left(\frac{3}{5}\times 90\right)=54°$
Supplement of $\frac{3}{5}\text{of a right angle}=\left(180-54\right)°=126°$

(iv) We know that $180°=179°60\text{'}$
Supplement of $75°36\text{'}=\left(179°60\text{'}-75°36\text{'}\right)$
$=104°24\text{'}$

(v) We know that $180°=179°59\text{'}60\text{'}\text{'}$
Supplement of $124°20\text{'}40\text{'}\text{'}=\left(179°59\text{'}60\text{'}\text{'}-124°20\text{'}40\text{'}\text{'}\right)$

Deg	Min	Sec
179	59	60
124	20	40
55	39	20

Hence, the measure of the required angle$=55°39\text{'}20\text{'}$.

(vi) We know that $180=179°59\text{'}60\text{'}\text{'}$
Supplement of $108°48\text{'}32\text{'}\text{'}=\left(179°59\text{'}60\text{'}\text{'}-108°48\text{'}32\text{'}\text{'}\right)$

Deg	Min	Sec
179	59	60
108	48	32
71	11	28

Hence, the measure of the required angle$=71°11\text{'}28\text{'}\text{'}$.