One angle of an octagon is \(100^{\circ}\) while the other sides are equal. Find each of these exterior angles ____________
A. \(80^{\circ}\) B. \(60^{\circ}\) C. \(140^{\circ}\) D. \(40^{\circ}\)
Correct Answer: D
Explanation
sum of the interior angle is \((n-2) 180^{\circ}=100^{\circ}+7 x\). where \(x\) is each equal angle for octagon, \(n=8^{\circ}\) \((8-2) 180^{\circ}=100^{\circ}+7 x\) \(6 \times 180^{\circ}=100^{\circ}+7 x: \quad 1080^{\circ}=100^{\circ}+7 x\) \(1080-100=7 x\) \(x=\frac{980}{7}=140^{\circ}\) but the interior angle \(+\) exterior angle \(=180^{\circ}\) (sum of angle on a straight line) \(\therefore\) The exterior angle is \(180^{\circ}-140^{\circ}=40^{\circ}\)