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WAEC 2018 Mathematics · Question 22

The angles of a polygon are x, 2x, 2x, (x + 30o30^o), (x + 20o20^o) and (x - 10o10^o). Find the value of x

Options

  1. A.45o45^o
  2. B.95o95^o
  3. C.84o84^o
  4. D.85o85^o

Answer: D. 85o85^o

Explanation written with AI and checked against the answer key

Analyze the question: The polygon has 6 angles, so it is a hexagon. We need x from the sum of its interior angles. Concept: The sum of interior angles of an n-sided polygon is (n − 2) × 180°. For n = 6: (6 − 2) × 180° = 4 × 180° = 720°. Solution: Add all the angles: x + 2x + 2x + (x + 30°) + (x + 20°) + (x − 10°) = 720° Collect the x terms: x + 2x + 2x + x + x + x = 8x Collect the constants: 30° + 20° − 10° = 40° So: 8x + 40° = 720° 8x = 680° x = 85° Check: The angles are 85, 170, 170, 115, 105, 75. Their sum is 85 + 170 + 170 + 115 + 105 + 75 = 720°. ✓ Answer: x = 85°, which is option D. Tip: For polygon questions, first count the angles to get n, then use (n − 2) × 180°. Always substitute x back to check that the angles add up to the total.

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