Question

The degree measure of each of the three angles of a triangle is an integer. Which of the following could not be the ratio of their measures ?

• A. $2:3:4$
• B. $3:4:5$
• C. $5:6:7$
• D. $6:7:8$

Answer 1

The correct option is D $6:7:8$

The following ratios are
A) 2:3:4
2 + 3 + 4 $=$ 9
9x $=$ 180
x $=$20
angles 40, 60, 80 total = 180
B) 3:4:5
12x $=$ 180
x $=$ 15
angles 45,60, 75 total is not 180 not a triangle
C) 5:6:7
18x $=$ 180
x $=$ 10
angle 50, 60, 70 total = 180
D) 6:7:8
21x $=$ 180
x $=$ 8.5714
angle 51.4285, 60, 68.5714 total $=$ 179.9989
Hence option D cant be the ratios of the measures