Question

The interior angles of an octagon are in A.P. The smallest angle is ${30}^{\circ }$ and the common difference is ${30}^{\circ }$.Find the sum of all the angles.

Answer 1

$a={30}^{\circ },d={30}^{\circ }$

Sum of interior angles$=\frac{n}{2}[2a+(n-1)d]$

$=\frac{8}{2}[2\times {30}^{\circ }+(8-1){30}^{\circ }]$

$=4[{60}^{\circ }+{210}^{\circ }]$

$=4\times {270}^{\circ }$

$={1080}^{\circ }$

$\therefore$ Sum of interior angles$={1080}^{\circ }$