Express each of the following angles in degrees.

Solution:

(i) Formula : Angle in degrees $=$ Angle in degrees $\times \frac{\pi}{180}$

Therefore, Angle in degrees $=\frac{5 \pi}{12} \times \frac{180}{\pi}=75^{\circ}$

(ii) Formula : Angle in degrees $=$ Angle in radians $\times \frac{180}{\pi}$

Therefore, Angle in degrees $=-\frac{18 \pi}{5} \times \frac{180}{\pi}=-648^{\circ}$

The angle in minutes = Decimal of angle in radian $\times 60 .^{\prime}$

The angle in seconds = Decimal of angle in minutes $\times 60 . "$

Therefore, Angle in degrees $=\frac{\frac{5}{6}}{6} \times \frac{180}{\pi}=\frac{150}{22 / 7}=47.7272^{\circ}$

Angle in minutes $=0.7272 \times 60^{\prime}=43.632^{\prime}$

Angle in seconds $=0.632 \times 60^{\prime \prime}=37.92^{\prime \prime}$

Final angle $=47^{\circ} 43^{\prime} 38^{\prime \prime}$

(iv) Formula: Angle in degrees $=$ Angle in radians $\times \frac{180}{\pi}$

The angle in minutes = Decimal of angle in radian $\times 60$.

The angle in seconds = Decimal of angle in minutes $\times 60 . "$

Therefore, Angle in degrees $=-4 \times \frac{180}{\pi}=-\frac{720}{22 / 7}=-229.0909^{\circ}$

Angle in minutes $=0.0909 \times 60^{\prime}=5.4545^{\prime}$

Angle in seconds $=0.4545 \times 60^{\prime \prime}=27.27^{\prime \prime}$

Final angle $=-229^{\circ} 5^{\prime} 27^{\prime \prime}$