Question

The degree measure of each of the three angles of a triangle is an integer. Which of the following CANNOT be the ratio of their measures?
2:3:4
3:4:5
4:5:6
5:6:7
6:7:8

Answer 1

@amistre64

Answer 2

the angles add up to 180 deg

to divide into ratios oyu add the proportions
e.g. the first one is 2/9:3/9:4/9

since the answers are all integers this can only be true if the denominator divides into 180 exactly

Answer 3

another method (i dunno if it's the right term for this) is that you could get the sum of the proportions and divide it to 180

Since a:b:c, and the measures are integers, then there exist an integer X such that aX + bX + cX = 180
X (a+b+c) = 180
X = 180/ (a+b+c)
If you got X as a whole number then it's a possible measure. If not, that's the wrong answer

Answer 4

that is the same method - but described in a different way

Answer 5

Okay. Thank you.

Answer 6

;)