Step 1 :A regular octagon is a polygon with 8 equal sides and 8 equal angles.
Step 2 :The formula to find the measure of each interior angle of a regular polygon is given by: \[\text{Interior Angle} = \frac{(n-2) \times 180}{n}\] where n is the number of sides of the polygon.
Step 3 :In this case, n = 8.
Step 4 :Substitute n = 8 into the formula: \[\text{Interior Angle} = \frac{(8-2) \times 180}{8} = 135.0^\circ\]
Step 5 :Final Answer: The measurement of each interior angle of a regular octagon is \(\boxed{135}^\circ\).