Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryMedium
A designer is creating a tile pattern using regular octagons. If one interior angle of a regular octagon is 135 degrees, what is the measure of one exterior angle?
- A30 degrees
- B90 degrees
- C60 degrees
- D45 degrees
Show answer & explanationAnswer & explanation
Correct answer: D. 45 degrees
An interior angle and its corresponding exterior angle of any polygon are supplementary, meaning they add up to 180 degrees. If the interior angle is 135 degrees, then the exterior angle is 180 - 135 = 45 degrees.
Why the other options are wrong
- A. Incorrect. This would be the exterior angle if the interior angle was 150 degrees.
- B. Incorrect. This is a right angle, not related to an octagon's exterior angle in this manner.
- C. Incorrect. This would be the exterior angle if the interior angle was 120 degrees.
Interior and Exterior Angles of a Polygon
An interior angle is an angle inside a polygon, formed by two adjacent sides. An exterior angle is formed by one side of a polygon and the extension of an adjacent side.
- An interior angle and its adjacent exterior angle are supplementary (add to 180°).
- The sum of all exterior angles of any convex polygon is 360°.
- For a regular n-sided polygon, each interior angle = (n-2) * 180 / n.
Memory trick: Interior is 'In', Exterior is 'Out', Together they make a 'Straight' line.