Four of the angles of a hexagon sum up to 420º. If the remaining angles are equal, find the value of each of the angles.

Analyze the question: A hexagon has 6 angles. Four of them add up to 420°, and the other two are equal. We need to find each of those two equal angles.

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

Solution:

1. Sum of interior angles of a hexagon = (6 − 2) × 180° = 4 × 180° = 720°
2. Four angles sum to 420°, so the remaining two angles sum to 720° − 420° = 300°
3. The two remaining angles are equal, so each is 300° ÷ 2 = 150°

Check: 420° + 150° + 150° = 720° ✓

Answer: Each of the remaining angles is 150°, which is option D.

Tip: For any polygon question, start by writing down the angle sum formula (n − 2) × 180°. Then subtract the known angles and divide the remainder by the number of equal angles left. Memorize the hexagon total of 720° because it appears often in exams.