Question

Measure of some angles are given below. Find the measure of their Complementary angles.
(i) 58$°$
(ii) 16$°$
(iii) $\frac{2}{3}rd$ of a right angle
(iv) (a+b)$°$
(v) (90 $-$ r)$°$
(vi) 48$°$ 36$\text{'}$ 24$\text{'}\text{'}$
(vii) 68$°$ 35$\text{'}$ 45$\text{'}\text{'}$
(viii) 56$°$ 43$\text{'}$ 20$\text{'}\text{'}$

Answer 1

$$\begin{gathered} \left(\mathrm{i}\right)58° \\ \mathrm{Its}\mathrm{complement}=90°-58°=32° \end{gathered}$$

$$\begin{gathered} \left(\mathrm{ii}\right)16° \\ \mathrm{Its}\mathrm{complement}=90°-16°=74° \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iii}\right)\frac{2}{3}\mathrm{rd}\mathrm{of}\mathrm{a}\mathrm{right}\mathrm{angle} \\ \mathrm{i}.\mathrm{e}.,\frac{2}{3}\times 90°=60° \\ \therefore \mathrm{Its}\mathrm{complement}=90°-60°=30° \end{gathered}$$

$$\begin{gathered} \left(\mathrm{iv}\right)\left(a+b\right)° \\ \mathrm{Its}\mathrm{complement}=90°-\left(a+b\right)°=\left(90-a-b\right)° \end{gathered}$$

$$\begin{gathered} \left(v\right)\left(90-r\right)° \\ \mathrm{Its}\mathrm{complement}=90°-\left(90-r\right)°=r° \end{gathered}$$

$$\begin{gathered} \left(\mathrm{vi}\right)48°36\text{'}24\text{'}\text{'} \\ \mathrm{Its}\mathrm{complement}=90°-\left(48°36\text{'}24\text{'}\text{'}\right) \\ =\left(89°59\text{'}60\text{'}\text{'}\right)-\left(48°36\text{'}24\text{'}\text{'}\right) \\ =\left(89°-48°\right)\left(59\text{'}-36\text{'}\right)\left(60\text{'}\text{'}-24\text{'}\text{'}\right) \\ =41°23\text{'}36\text{'}\text{'} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{vii}\right)68°35\text{'}45\text{'}\text{'} \\ \mathrm{Its}\mathrm{complement}=90°-\left(68°35\text{'}45\text{'}\text{'}\right) \\ =\left(89°59\text{'}60\text{'}\text{'}\right)-\left(68°35\text{'}45\text{'}\text{'}\right) \\ =\left(89°-68°\right)\left(59\text{'}-35\text{'}\right)\left(60\text{'}\text{'}-45\text{'}\text{'}\right) \\ =21°24\text{'}15\text{'}\text{'} \end{gathered}$$

$$\begin{gathered} \left(\mathrm{vii}\right)56°43\text{'}20\text{'}\text{'} \\ \mathrm{Its}\mathrm{complement}=90°-\left(56°43\text{'}20\text{'}\text{'}\right) \\ =\left(89°59\text{'}60\text{'}\text{'}\right)-\left(56°43\text{'}20\text{'}\text{'}\right) \\ =\left(89°-56°\right)\left(59\text{'}-43\text{'}\right)\left(60\text{'}\text{'}-20\text{'}\text{'}\right) \\ =33°16\text{'}40\text{'}\text{'} \end{gathered}$$