Regular polygons

Two regular polygons, x and y, are such that the number of sides of x is three more than the number of the sides of y. If the sum of the exterior angles of x and y is 117°, how many sides have x?

Correct answer:

x =  8

Step-by-step explanation:

α = n360°  x=3+y x360° + y360° = 117° 360°/x + 360°/(x3) = 117°  360(x3)+360x=117 x (x3)  360(x3)+360x=117 x (x3) 117x2+1071x1080=0 117x21071x+1080=0 117=3213 1071=32717 1080=23335 GCD(117,1071,1080)=32=9  13x2119x+120=0  a=13;b=119;c=120 D=b24ac=1192413120=7921 D>0  x1,2=2ab±D=26119±7921 x1,2=26119±89 x1,2=4.576923±3.423077 x1=8 x2=1.153846154  x=x1=8  y=x3=83=5

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