Question

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

• A. , , ,
• B. , , ,
• C. , , ,
• D. , , ,

Answer 1

The correct option is B , , ,

Suppose that $\angle A=x\circ$, then $\angle B=x+{10}^{\circ }$,
$\angle C=x+{20}^{\circ }$ and $\angle D=x+{30}^{\circ }$
So, we know that $\angle A+\angle B+\angle C+\angle D=2\pi$ Putting these values, we get
$\left(x^{\circ }\right)+(x^{\circ }+{10}^{\circ })+(x^{\circ }+{20}^{\circ })+(x^{\circ }+{30}^{\circ })={360}^{\circ }$
$\Rightarrow x={75}^{\circ }$
Hence the angles of the quadrilateral are ${75}^{\circ },{85}^{\circ },{95}^{\circ },{105}^{\circ }.$