The angles of a quadrilateral are in AP, and the greatest angle is double the least. Express the least angle in radians.
Let the smallest term be x, and the largest term be 2x
Then AP formed= x, ?, ?, 2x
So
$\mathrm{S}_{\mathrm{n}}=\frac{\mathrm{n}}{2}[2 \mathrm{a}+(\mathrm{n}-1) \mathrm{d}]$
$\mathrm{S}_{\mathrm{n}}=\frac{\mathrm{n}}{2}[\mathrm{a}+(\mathrm{a}+(\mathrm{n}-1) \mathrm{d})]=\frac{\mathrm{n}}{2}[$ First term $+($ Last term $)]$
$360^{\circ}=4 / 2[x+2 x] \ldots . .[$ We know that $\rightarrow a+(n-1) d=$ last term $=2 x]$
$\Rightarrow 180^{\circ}=3 x$
$\Rightarrow x=60^{\circ}$
Now, $60^{\circ}$ is least angle.
$=60^{\circ}=\pi / 180^{\circ} \times 60^{\circ}$
$\Rightarrow 60^{\circ}=\pi / 3 \mathrm{rad}$
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