In a regular pentagon, each interior angle measures how many degrees?

In a regular pentagon, each interior angle measures how many degrees?

• A. 108 degrees
• B. 72 degrees
• C. 120 degrees
• D. 135 degrees

Answer: (A)

In a regular polygon, all interior angles are equal, and the total sum of interior angles is (n−2)×180, where n is the number of sides. For a pentagon, n = 5, so the total is (5−2)×180 = 540 degrees. Since there are five equal interior angles, each one measures 540 ÷ 5 = 108 degrees. So the interior angle is 108 degrees. The other numbers relate to different angles in a pentagon: 72 degrees is the central angle between adjacent vertices (360/5), while 120 and 135 degrees are interior angles of polygons with more sides (hexagon and octagon, respectively).

In a regular polygon, all interior angles are equal, and the total sum of interior angles is (n−2)×180, where n is the number of sides. For a pentagon, n = 5, so the total is (5−2)×180 = 540 degrees. Since there are five equal interior angles, each one measures 540 ÷ 5 = 108 degrees. So the interior angle is 108 degrees. The other numbers relate to different angles in a pentagon: 72 degrees is the central angle between adjacent vertices (360/5), while 120 and 135 degrees are interior angles of polygons with more sides (hexagon and octagon, respectively).