How many sides does a regular polygon have if each exterior angle measures 72
1 answer:
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Answer:
x = 1/2
Step-by-step explanation:
The sum of numbers in all rows, columns and diagonals have to be the same.
Notice the diagonals do not have an x so let's sum those numbers to see what the sum for all must be.
-2+(1/2) +3 = (-4+1+6)/2 = 3/2
-5+(1/2)+6 = (-10+1+12)/2 = 3/2
Now we can pick the first row and sum the numbers up knowing that the result should be 3/2, will find x
-2+x-3+6 = 3/2, combine like terms
x+1 = 3/2 , subtract 1 from both sides
x = (3/2)-1, find common denominator and subtract
x = (3-2)/2, combine like terms
x = 1/2
Check or work:
Rows from top to down
-2 +(1/2) -3 +6 = (-4+1-6+12)/2 = 3/2✅
17*(1/2) +(1/2) +(1/2)-8 = (17+1+1-16)/2 = 3/2✅
-5+(9/2) -2(1/2) +3 = (-10+9-2+6)/2 = 3/2✅
Columns from left to right
-2+17(1/2)-5 = (-4+17-10)/2 =3/2✅
(1/2)-3+(1/2)+(9/2)-2(1/2) = (1-6+1+9-2)/2 = 3/2✅
6+(1/2)-8+3 = (12+1-16+6)/2 = 3/2✅
Diagonals
-2+(1/2) +3 = (-4+1+6)/2 = 3/2✅
-5+(1/2)+6 = (-10+1+12)/2 = 3/2✅
