Final answer:
The angle of a regular polygon with 40 sides is 171° and in radians, it is approximately 3π/2 or about 3.14/2.
Step-by-step explanation:
Finding the Angle of a Regular Polygon
To express in radians and also in degrees the angle of a regular polygon, we use the formula for the interior angle of a regular polygon, which can be found by dividing the total sum of the interior angles by the number of sides.
The total sum of the interior angles of a polygon is (n-2) × 180°, where n is the number of sides of the polygon. For a regular polygon with 40 sides, it would be (40-2) × 180° = 38 × 180°. Dividing this by 40 gives us the measure of each interior angle.
38 × 180° / 40 = 171°. To convert this angle into radians, we use the fact that π radians = 180°. Therefore, 171° in radians is 171/180 × π = 3π/2 (approximately 3.14/2).