The interior angles of a polygon are 3x$^o$, 2x$^o$, 4x$^o$, 3x$^o$ and 6x$^o$. Find the size of the smallest angle of the polygon.

Analyze the question: The polygon has 5 angles, so it is a pentagon. We need the smallest interior angle.

Concept: The sum of the interior angles of an n-sided polygon is (n − 2) × 180°.

Solution:

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

Add the given angles: 3x + 2x + 4x + 3x + 6x = 18x

Set them equal: 18x = 540 x = 30

The angles are:

• 3x = 90°
• 2x = 60°
• 4x = 120°
• 3x = 90°
• 6x = 180°

Check: 90 + 60 + 120 + 90 + 180 = 540° ✓

The smallest angle is 2x = 60°.

(One note: an interior angle of 180° is a straight angle, so the shape is technically degenerate. But the question is written this way, and the answer still follows from the calculation.)

Answer: The smallest angle is 60°, which is option B.

Tip: For polygon angle questions, always begin with (n − 2) × 180°, add up the algebraic terms, solve for x, then substitute back. Remember to pick the smallest coefficient. Here it is 2x, not x, so the answer is 2 × 30, not 30.