Question

If all the angles of an octagon are equal, find the measure of each angle.

Answer 1

Number of sides of octagon, n = 8
Let us consider each angle be $x^{\circ }$
We know that,
The sum of all the interior angles of octagon = $8x^{\circ }$
The sum of all the interior angles of a polygon $=(2n-4)\times {90}^{\circ }$
The sum of interior angles of polygon can be calculated as,
$(2n-4)\times {90}^{\circ }$ = Sum of angles
$(2n-4)\times {90}^{\circ }=8x^{\circ }$
$(2\times 8-4)\times {90}^{\circ }=8x^{\circ }12\times {90}^{\circ }=8x^{\circ }x=\frac{12\times {90}^{\circ }}{8}\text{We get},x={135}^{\circ }$
Therefore, each angle of octagon = ${135}^{\circ }$