Geometry and TrigonometryEasy–MediumInterior angles of a polygon
Geometry and Trigonometry practice question
What is the sum of the measures of the interior angles of a pentagon?
- A. 540°Correct
- B. 360°
- C. 720°
- D. 180°
Answer: A. 540°
A polygon with n sides can be cut into n − 2 triangles from one vertex, each contributing 180°. For a pentagon, (5 − 2) × 180° = 540°.
Why the other answers are wrong
- B. 360°
- 360° is the interior angle sum of a QUADRILATERAL (four sides). A pentagon has one more triangle's worth.
- C. 720°
- 720° is the sum for a hexagon, (6 − 2) × 180°.
- D. 180°
- 180° is the sum for a single triangle. A pentagon contains three of them.
More Geometry and Trigonometry questions
- Easy–Medium
A circle has a radius of 6. What is its area? (Use A = πr².) - Easy–Medium
A right triangle has legs of length 6 and 8. What is the length of the hypotenuse? - Easy–Medium
A circle has a radius of 5. What is its circumference? (Use C = 2πr.) - Easy–Medium
What is the midpoint of the segment joining the points (2, 3) and (8, 11)? - Easy–Medium
What is the measure, in degrees, of angle B? - Easy–Medium
What is the area, in square centimeters, of the trapezoid?
Not affiliated with the College Board. SAT is a trademark of the College Board.