A 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
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Answer:
(D) 6:7:8
Step-by-step explanation:
Given that the degree measure of each of the three angles of a triangle is an integer.
We know the sum of the angles of a triangle is 180°.
So, consider the common ratio is x.
Now,
(A) 2x + 3x + 4x = 180°
=> 9x = 180°
=> x = 180°/9
=> x = 20° is an integer
(B) 3x + 4x + 5x = 180°
=> 12x = 180°
=> x = 180°/12
=> x = 15° is an integer
(C) 5x + 6x + 7x = 180°
=> 18x = 180°
=> x = 180°/18
=> x = 18° is an integer
(D) 6x + 7x + 8x = 180°
=> 21x = 180°
=> x = 180°/21
=> x = 60°/7 is not an integer
Hence, 6:7:8 could not be the ratio of their measures
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