Question on: WAEC Mathematics - 2017
Three exterior angles of a polygon are 30\(^o\), 40\(^o\) and 60\(^o\). If the remaining exterior angles are 46\(^o\) each, name the polygon.
A
decagon
B
nonagon
C
octagon
D
hexagon
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Correct Option: C
The sum of the exterior angles of any polygon is always 360 degrees. Let's calculate the sum of the given exterior angles and determine the number of sides.
1. **Sum of known exterior angles:** 30\(^o\) + 40\(^o\) + 60\(^o\) = 130\(^o\)
2. **Let *n* be the number of remaining angles, each being 46\(^o\):** 46\(^o\) * n
3. **Total sum of exterior angles:** 130\(^o\) + 46\(^o\) * n = 360\(^o\)
4. **Solve for *n*:**
* 46n = 360 - 130
* 46n = 230
* n = 230 / 46
* n = 5
5. **Total number of exterior angles (and sides):** 3 + 5 = 8
Since the polygon has 8 sides, it is an octagon.
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