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In the figure above, x = y/2, and z = 3y/8. What is the degree measure

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In the figure above, x = y/2, and z = 3y/8. What is the degree measure  [#permalink]

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New post 08 Aug 2017, 10:26
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87% (01:41) correct 13% (01:37) wrong based on 32 sessions

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Re: In the figure above, x = y/2, and z = 3y/8. What is the degree measure  [#permalink]

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New post 08 Aug 2017, 11:21
Bunuel wrote:
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In the figure above, x = y/2, and z = 3y/8. What is the degree measure of the smallest angle of the triangle?

(A) 96
(B) 72
(C) 48
(D) 36
(E) 12

Attachment:
2017-08-08_2125.png


Sum of angles of triangle \(= 180^{\circ}\)

\(x + y + z = 180\)

Given; \(x = \frac{y}{2}\), and \(z = \frac{3y}{8}\)

\(\frac{y}{2} + y + \frac{3y}{8} = 180\)

\(\frac{4y + 8y + 3y}{8} = 180\)

\(15y = 180 * 8\)

\(y = \frac{180 * 8}{15} => 96\)

\(x = \frac{y}{2} = \frac{96}{2} => 48\)

\(z = \frac{3y}{8} = \frac{3*96}{8} => 36\)

Therefore, degree measure of the smallest angle of the triangle \(= 36\)

Answer (D)...
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Re: In the figure above, x = y/2, and z = 3y/8. What is the degree measure  [#permalink]

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New post 08 Aug 2017, 22:20
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Since x = \(\frac{y}{2}\), we can say that y = 2x
Since z = \(\frac{3y}{8}\) we can say that z = \(\frac{3(2x)}{8}\) = \(\frac{3x}{4}\)

We know that x+y+z = 180
Substituting these values, we have \(x + 2x + \frac{3x}{4} = 3x + \frac{3x}{4} = 180\)
\(3x + \frac{3x}{4} = 3x(1+\frac{1}{4}) = 3x(\frac{5}{4}) = 180\)
\(3x = 180*\frac{4}{5}\)
Therefore, \(x = \frac{180*4}{5*3} = 12*4 = 48\)

The smallest angle is \(\frac{3x}{4} = \frac{3}{4}*48\) = 36(Option D)

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Re: In the figure above, x = y/2, and z = 3y/8. What is the degree measure   [#permalink] 08 Aug 2017, 22:20
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