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If the degree measures of the interior angles of a triangle are x, y,
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21 Dec 2021, 05:21
21 Dec 2021, 05:21
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If the degree measures of the interior angles of a triangle are x, y, and z, where x = y/4 = 3z/5, what is the value of z?
(A) 20
(B) 30
(C) 45
(D) 60
(E) 100
(A) 20
(B) 30
(C) 45
(D) 60
(E) 100
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Posts: 6218
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If the degree measures of the interior angles of a triangle are x, y,
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21 Dec 2021, 07:06
21 Dec 2021, 07:06
1
Carcass wrote:
If the degree measures of the interior angles of a triangle are x, y, and z, where x = y/4 = 3z/5, what is the value of z?
(A) 20
(B) 30
(C) 45
(D) 60
(E) 100
(A) 20
(B) 30
(C) 45
(D) 60
(E) 100
Let's rewrite each angle in terms of x.
Given: x = y/4
Multiply both sides of the equation by 4 to get: 4x = y
Also given: x = 3z/5
Multiply both sides of the equation by 5 to get: 5x = 3z
Divide both sides of the equation by 3 to get: 5x/3 = z
Since the three angles in a triangle must add to 180° we can write: x + y + z = 180
Substitute values to get: x + 4x + 5x/3 = 180
Eliminate the fraction by multiplying both sides of the equation by 3 to get: 3x + 12x + 5x = 540
Simplify to get: 20x = 540
Solve: x = 540/20 = 27
Now that we know x = 27, we can take the given equation: x = 3z/5
And substitute to get: 27 = 3z/5
Multiply both sides of the equation by 5 to get: 135 = 3z
Divide both sides of the equation by 3 to get: 45 = z
Answer: C
gmatclubot
If the degree measures of the interior angles of a triangle are x, y, [#permalink]
21 Dec 2021, 07:06
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