Question

If the angles of a quadrilateral are in A.P. whose common difference is ${10}^{\circ }$, then find the angles of the quadrilateral.

Answer 1

Suppose that ∠A = x, then ∠B = x + ${10}^{\circ }$,

$\angle C$ = x + ${20}^{\circ }$ and ∠D = x + ${30}^{\circ }$

So, we know that ∠A + ∠B + ∠C + ∠D = $2\pi$

Putting these values , we get

$\left(x\right)$ + ( $x+{10}^{\circ }$) + ( $x+{20}^{\circ }$) + ( $x+{30}^{\circ }$) = ${360}^{\circ }$

$\Rightarrow x=$ ${75}^{\circ }$

Hence, the angles of the quadrilateral are ${75}^{\circ }$, ${85}^{\circ }$, ${95}^{\circ }$, ${105}^{\circ }$.