Question

The angels of quadrilateral are in A.P. and the greatest angel is double the least, find angels of the quadrilateral in radian?

a-d,a-2d,a+d,a+2d​

Answer 1

Answer:

Angles in radian $\frac{5\pi}{16},\frac{7\pi}{16},\frac{9\pi}{16}$ and $\frac{11\pi}{16}$

Step-by-step explanation:

Let $a-3d,a-d,a+d,a+3d$ are the angles of quadrilateral in A.P.

Given, greatest angle is twice of least angle

 $\Rightarrow a+3d=2(a-3d)\Rightarrow a+3d=2a-6d\Rightarrow a=8d\Rightarrow d=\frac{a}{8}$

But we know that, sum of all the interior angles of quadrilateral is $2\pi$

$\Rightarrow a-3d+a-d+a+d+a+3d=2\pi$

$\Rightarrow 4a=2\pi \Rightarrow a=\frac{\pi}{2}$$\therefore d=\frac{a}{8}=\frac{\pi}{16}$

Thus angles are,

$a-3d=\frac{\pi}{2}-\frac{3\pi}{16}=\frac{5\pi}{16}, a-d=\frac{\pi}{2}-\frac{\pi}{16}=\frac{7\pi}{16}$

$a+d=\frac{\pi}{2}+\frac{\pi}{16}=\frac{9\pi}{16}, a+3d=\frac{\pi}{2}+\frac{3\pi}{16}=\frac{11\pi}{16}$