Question

If the angles of a triangle are in A.P., then the measures of one of the angles in radians is

• A. $\frac{\pi }{6}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{2}$
• D. $\frac{2\pi }{3}$

Answer 1

The correct option is B

$\frac{\pi }{3}$

Let the angles of the triangle be $(a-d{)}^{\circ }$, $(a{)}^{\circ }$ and $(a+d{)}^{\circ }$

Thus, we have:

a - d + a + a + d = 180

$\Rightarrow$ 3a = 180

$\Rightarrow$ a = 60

Hence, the angles are $(a-d{)}^{\circ },(a{)}^{\circ }and(a+d{)}^{\circ }i.e.(60-d{)}^{\circ },\left(60{)}^{\circ }and\right(60+d{)}^{\circ }{60}^{\circ }$ is the only angle which is independent of d.

$\therefore$ One of the angles of the triangle (in radians)$=(60\times \frac{\pi }{180})=\frac{\pi }{3}$