Praxis Core Academic Skills for Educators: Mathematics (5733)GeometryEasy
A designer is creating a logo that involves a regular pentagon. If the sum of the interior angles of a regular polygon is given by the formula (n-2) × 180°, where 'n' is the number of sides, what is the measure of one interior angle of this regular pentagon?
- A144°
- B120°
- C72°
- D108°
Show answer & explanationAnswer & explanation
Correct answer: D. 108°
A pentagon has 5 sides (n=5). First, calculate the sum of the interior angles using (n-2) × 180°. Then, divide this sum by the number of sides (n) to find the measure of one interior angle of a regular pentagon.
Why the other options are wrong
- A. This is incorrect; it is the interior angle of a regular decagon, not a pentagon.
- B. This is incorrect; it is the interior angle of a regular hexagon, not a pentagon.
- C. This is the measure of an exterior angle of a regular pentagon, not an interior angle.
Interior Angle of Regular Polygon
The angle formed by two adjacent sides inside a regular polygon, where all interior angles are equal.
- Sum of interior angles: (n-2) × 180°.
- For a regular polygon, all interior angles are equal.
- One interior angle = (Sum of interior angles) / n.
Memory trick: Count the 'n' sides, subtract '2' for triangles, then '180' for degrees!