what is the measure of each interior angle of a regular octagon? 45° 60° 120° 135°
what is the measure of each interior angle of a regular octagon? 45° 60° 120° 135°
Answer
Explanation:
Step1: Find the sum of interior angles
The formula for the sum of interior angles of a polygon is ((n - 2)\times180^{\circ}), where (n) is the number of sides. For an octagon, (n = 8). [ \begin{align*} S&=(8 - 2)\times180^{\circ}\ &=6\times180^{\circ}\ &=1080^{\circ} \end{align*} ]
Step2: Calculate the measure of each interior angle
Since it is a regular octagon (all interior angles are equal), divide the sum (S) by (n). [ \begin{align*} \text{Each interior angle}&=\frac{1080^{\circ}}{8}\ &=135^{\circ} \end{align*} ]
Answer:
(135^{\circ}) (the fourth option)