Here are the solutions to the problems on your worksheet.
1. Sum of Exterior Angles Table
To find each exterior angle of a regular polygon, you divide $360^\circ$ by the number of sides.
a) Hexagon (6 sides)
* Calculation: $360 \div 6 = 60$
* Each exterior angle =
$60^\circ$
b) Octagon (8 sides)
* Calculation: $360 \div 8 = 45$
* Each exterior angle =
$45^\circ$
c) Nonagon (9 sides)
* Calculation: $360 \div 9 = 40$
* Each exterior angle =
$40^\circ$
d) 15-gon (15 sides)
* Calculation: $360 \div 15 = 24$
* Each exterior angle =
$24^\circ$
e) 24-gon (24 sides)
* Calculation: $360 \div 24 = 15$
* Each exterior angle =
$15^\circ$
f) 40-gon (40 sides)
* Calculation: $360 \div 40 = 9$
* Each exterior angle =
$9^\circ$
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2. Find the value of the missing angles
The rule is that the sum of exterior angles for any polygon is always $360^\circ$. We add the known angles together and subtract that total from $360^\circ$ to find the missing one.
(a)
* Equation: $x + 101^\circ + 112^\circ = 360^\circ$
* Add the knowns: $101 + 112 = 213$
* Subtract from 360: $360 - 213 = 147$
*
$x = 147^\circ$
(b)
* Equation: $R + 60^\circ + 77^\circ + 75^\circ + 131^\circ = 360^\circ$
* Add the knowns: $60 + 77 + 75 + 131 = 343$
* Subtract from 360: $360 - 343 = 17$
*
$R = 17^\circ$
(c)
* Equation: $a + 100^\circ + 120^\circ = 360^\circ$
* Add the knowns: $100 + 120 = 220$
* Subtract from 360: $360 - 220 = 140$
*
$a = 140^\circ$
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Final Answer:
1. Table Values:
* a) $60^\circ$
* b) $45^\circ$
* c) $40^\circ$
* d) $24^\circ$
* e) $15^\circ$
* f) $9^\circ$
2. Missing Angles:
* (a) $x = 147^\circ$
* (b) $R = 17^\circ$
* (c) $a = 140^\circ$
Parent Tip: Review the logic above to help your child master the concept of interior angles of a polygon worksheet.
