Find the sum of the interior angle of a pentagon.

Analyze the question: You need the total of all the interior angles of a pentagon (a 5-sided polygon).

Concept: The sum of the interior angles of an n-sided polygon is

Sum = (n − 2) × 180°

This works because any polygon can be split into (n − 2) triangles by drawing diagonals from one vertex. Each triangle has angles that add up to 180°.

Solution:

For a pentagon, n = 5:

Sum = (5 − 2) × 180° Sum = 3 × 180° Sum = 540°

Checking by triangles: from one vertex of a pentagon you can draw 2 diagonals, which split it into 3 triangles. So 3 × 180° = 540°. ✔

Matching the options:

• A. 340° ✗
• B. 350° ✗
• C. 540° ✔
• D. 550° ✗

Tip: Memorize the formula (n − 2) × 180°. Some quick values: triangle 180°, quadrilateral 360°, pentagon 540°, hexagon 720°. Each extra side adds 180°. Also, for a regular pentagon, each interior angle is 540° ÷ 5 = 108°, which often appears in follow-up questions.