Question

Measures of some angles are given below. Find the measures of their supplementary angles.
(i) 60$°$
(ii) 138$°$
(iii) $\frac{3}{5}th$of a right angle
(iv) (180 $-$ r)$°$
(v) (90 + r)$°$
(vi) 87$°$ 20$\text{'}$ 43$\text{'}\text{'}$
(vii) 124$°$ 28$\text{'}$ 40$\text{'}\text{'}$
(viii) 108$°$ 48$\text{'}$ 32$\text{'}\text{'}$

Answer 1

(i) $60°$
Its supplement = $180°-60°=120°$

(ii) 138$°$
Its supplement = $180°-138°=42°$

(iii)

$$\begin{gathered} \frac{3}{5}\mathrm{th}\mathrm{of}\mathrm{a}\mathrm{right}\mathrm{angle} \\ \mathrm{i}.\mathrm{e}.,\frac{3}{5}\times 90°=54° \end{gathered}$$

∴ Its supplement = $180°-54°=126°$

(iv) ${\left(180-r\right)}^{°}$

Its supplement = $180°-\left(180-r\right)°=r°$

(v) $\left(90+r\right)°$

$$\begin{gathered} \mathrm{Its}\mathrm{supplement}=180°-\left(90+r\right)°=180°-90°-r° \\ =\left(90-r\right)° \end{gathered}$$

(vi) $87°20\text{'}43\text{'}\text{'}$

$$\begin{gathered} \mathrm{Its}\mathrm{supplement}=180°-\left(87°20\text{'}43\text{'}\text{'}\right) \\ =\left(179°59\text{'}60\text{'}\text{'}\right)-\left(87°20\text{'}43\text{'}\text{'}\right) \\ =\left(179°-87°\right)\left(59\text{'}-20\text{'}\right)\left(60\text{'}\text{'}-43\text{'}\text{'}\right) \\ =92°39\text{'}17\text{'}\text{'} \end{gathered}$$

(vii) $124°28\text{'}40\text{'}\text{'}$

$$\begin{gathered} \mathrm{Its}\mathrm{supplement}=180°-\left(124°28\text{'}40\text{'}\text{'}\right) \\ =\left(179°59\text{'}60\text{'}\text{'}\right)-\left(124°28\text{'}40\text{'}\text{'}\right) \\ =\left(179°-124°\right)\left(59\text{'}-28\text{'}\right)\left(60\text{'}\text{'}-40\text{'}\text{'}\right) \\ =55°31\text{'}20\text{'}\text{'} \end{gathered}$$

(viii) $108°48\text{'}32\text{'}\text{'}$

$$\begin{gathered} \mathrm{Its}\mathrm{supplement}=180°-\left(108°48\text{'}32\text{'}\text{'}\right) \\ =\left(179°59\text{'}60\text{'}\text{'}\right)-\left(108°48\text{'}32\text{'}\text{'}\right) \\ =\left(179°-108°\right)\left(59\text{'}-48\text{'}\right)\left(60\text{'}\text{'}-32\text{'}\text{'}\right) \\ =71°11\text{'}28\text{'}\text{'} \end{gathered}$$