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2020 · Q71

In a triangle, values of all the angles are integers (in degree measure). Which one of the following cannot be the proportion of their measures?

Elementary MathematicsGeometry: Lines, Angles and Triangles
  1. A1:2:3
  2. B3:4:5
  3. C5:6:7
  4. D6:7:8

Explanation

The angles must be integers summing to 180: 1:2:3, 3:4:5 and 5:6:7 all work, but 180/(6+7+8) = 180/21 is not an integer. So 6:7:8 is impossible - option (D). 180/21 is not an integer, so no integer-degree triangle can have the ratio 6:7:8.