WAEC 2017 Mathematics · Question 16
Three exterior angles of a polygon are 30, 40 and 60. If the remaining exterior angles are 46 each, name the polygon.
Options
- A.decagon
- B.nonagon
- C.octagon
- D.hexagon
Answer: C. octagon
Explanation written with AI and checked against the answer key
Concept: The sum of the exterior angles of any polygon is 360°. A polygon with n sides has n exterior angles. Step 1: Add the known exterior angles 30° + 40° + 60° = 130° Step 2: Find what is left for the remaining angles 360° − 130° = 230° Step 3: Divide by 46° to find how many remaining angles there are 230° ÷ 46° = 5 Step 4: Count all the sides n = 3 + 5 = 8 sides A polygon with 8 sides is an octagon. Check: 130° + 5(46°) = 130° + 230° = 360° ✓ Tip: For questions like this, always start with "exterior angles add up to 360°". Subtract the known angles, divide by the repeated angle, then add back the number of known angles. Also remember the names: 5 pentagon, 6 hexagon, 7 heptagon, 8 octagon, 9 nonagon, 10 decagon.AI can make mistakes. Report anything that looks wrong.
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