# Geometry

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The three angles of a triangle have measures 12x degree, 3x degree, and 7y degree, where 7y>60. If x and y are integers, what is the value of x?

• Geometry -

12x + 3x + 7y = 180
15x + 7y = 180
15x + 60 < 180
15x < 120
x < 8

check:
pick a value of x,
1. x < 8 , e.g. let x = 4
then 48+12 + 7y = 180
7y = 120 , so 7y > 60 , OK!

2. x > 8 , e.g. x = 10
then 150 + 30 + 7y = 180
7y = 0 , and 7y > 60 is false

Therefore x < 8 is correct.

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