Q27
ArithmeticGeometry & Mensuration
If the measures of two angles of a triangle are 65°20′3″ and 54°39′57″, then the circular value of third angle is:
- a.$\pi^c$
- b.$\frac{\pi}{2}^c$
- c.$\frac{\pi}{3}^c$
- d.$\frac{2\pi}{3}^c$
Answer: (C) $\frac{\pi}{3}^c$
The two angles add to 65°20′3″ + 54°39′57″ = 120°0′0″, so the third angle is 180° − 120° = 60°. In radians (circular measure) 60° is $\frac{\pi}{3}$. $\frac{2\pi}{3}$ is the sum of the two given angles, not the third one.