Write the complement of each of the following angles :

(i) 46°

(ii) 90°

(iii) $\dfrac{3}{5}$ of a right angle

(iv) (x + 12)°

(v) 34° 27'

(vi) 42° 36' 25"

(i) 46°

Complement of 46° = 90° − 46° = 44°

Hence, the answer is 44°.

(ii) 90°

Complement of 90° = 90° − 90° = 0°

Hence, the answer is 0°.

(iii) $\dfrac{3}{5}$ of a right angle

First, let's find the angle:

$\dfrac{3}{5}$ of a right angle = $\dfrac{3}{5} \times 90^{\circ}$

= $\dfrac{3}{1} \times 18^{\circ}$

= 54°

Complement of 54° = 90° − 54° = 36°

Hence, the answer is 36°.

(iv) (x + 12)°

Complement of (x + 12)° = 90° − (x + 12)°

= 90° − x° - 12°

= 78° - x°

= (78 - x)°

Hence, the answer is (78 - x)°.

(v) 34° 27'

To subtract 27' from 0', we borrow 1° from the 90° and convert it into 60'.

Complement of 34° 27' = 90° − 34° 27'

= 89° 60' − 34° 27'

Thus,

$\begin{array}{rcc} 89^\circ & 60' \ -34^\circ & 27' \ \hline 55^\circ & 33' \ \hline \end{array}$

Complement of 34° 27' = 55° 33'

Hence, the answer is 55° 33'.

(vi) 42° 36' 25"

To subtract 25'' and 36' from 0'' and 0', we borrow 1° from the 90° to get 60', and then borrow 1' from that to get 60'', leaving 89° and 59'.

Complement of 42° 36' 25" = 90° − 42° 36' 25"

= 89° 59' 60" − 42° 36' 25"

Thus,

$\begin{array}{rrrc} 90° = 89^\circ & 59' & 60'' \ -42^\circ & 36' & 25'' \ \hline 47^\circ & 23' & 35'' \ \hline \end{array}$

Complement of 42° 36' 25" = 47° 23' 35"

Hence, the answer is 47° 23' 35".