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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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08 Aug 2017, 10:26
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Question Stats:

88% (01:14) correct 12% (01:26) wrong based on 26 sessions

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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

[Reveal] Spoiler:
Attachment:

2017-08-08_2125.png [ 6.04 KiB | Viewed 396 times ]
[Reveal] Spoiler: OA

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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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08 Aug 2017, 11:21
Bunuel wrote:

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

[Reveal] Spoiler:
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 $$= 36$$

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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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08 Aug 2017, 22:20

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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