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 sum of the terms of the given ratio should completely divide ${180}^{\circ }$, i.e., angle sum of a triangle.

For option A, $2+3+4=9$ divides ${180}^o$

For option B, $3+4+5=12$ divides ${180}^o$

For option C, $5+6+7=18$ divides ${180}^o$

But in option D, sum of terms of ratio $=6+7+8=21$, which does not completely divide ${180}^{\circ }$.

Hence, $6:7:8$ could not be the ratio of their measures.