# ACT Math 4.2 Plane Geometry

ACT Math: Plane Geometry Drill 4, Problem 2. If x, y, and z are all integer values, which of the following cannot be the ratio of x:y:z?

ACT Math | Plane Geometry |

ACT Mathematics | Plane Geometry |

Foreign Language | Arabic Subtitled Chinese Subtitled Korean Subtitled Spanish Subtitled |

Geometry | Triangles |

Language | English Language |

Plane Geometry | Properties of plane figures |

Product Type | ACT Math |

### Transcript

aren't fractions or decimals. We also know that

the sum of a triangle's angles always equal 180 degrees. So... since the ratios of the

angles are always relative to 180 degrees, we have to look for the ratio that can't

allow the angles to be integers. In English, that basically means that, since

we're dividing up 180 degrees into little parts...

...180 has to be divisible by the total number

of parts in the ratio. The question is asking for the ratio that

can't be possible, so we have to look for the one that isn't divisible by 180. Let's

try: A: 1 + 2 + 3 = 6 and 180 / 6 = 30

B: 1 + 2 + 2 = 5, 180 / 5 = 36 C: 1 + 1 + 2 = 4, 180 / 4 = 45

D: 1 + 2 + 4 = 7, 180 / 7 = 25.715 E: 1 + 2 + 6 = 9, 180 / 9 = 20

Our answer is D because it doesn't produce an integer value, which means that each part

is not an integer, which ultimately means that the angles can't be integers either.