Question

The angles of a triangle are in A.P and the least angle is ${30}^o$. What is the greatest angle (in radian)?

• A. $\frac{\pi }{2}$
• B. $\frac{\pi }{3}$
• C. $\frac{\pi }{4}$
• D. $\pi$

Answer 1

The correct option is A $\frac{\pi }{2}$

Let the angles be $A,B$ and $C$
As they are in A.P
So, $2B=A+C$ ........ $\left(i\right)$
Sum of angle of triangle
$A+B+C={180}^o$
From $\left(i\right)$, we get
$3B={180}^o$

$\Rightarrow B={60}^o$
The smallest angle is ${30}^o$
$\therefore A={30}^o$
So, the greatest angle $={180}^o-{60}^o-{30}^o={90}^o$
Hence, option A is correct.