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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. ### Request Expert Reply # In the figure above, x = y/2, and z = 3y/8. What is the degree measure

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Math Expert V
Joined: 02 Sep 2009
Posts: 55150
In the figure above, x = y/2, and z = 3y/8. What is the degree measure  [#permalink]

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Difficulty:   25% (medium)

Question Stats: 87% (01:41) correct 13% (01:37) wrong based on 32 sessions

### HideShow timer Statistics 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 [ 6.04 KiB | Viewed 650 times ]

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Director  V
Joined: 04 Dec 2015
Posts: 750
Location: India
Concentration: Technology, Strategy
WE: Information Technology (Consulting)
Re: In the figure above, x = y/2, and z = 3y/8. What is the degree measure  [#permalink]

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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

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)...
Senior PS Moderator V
Joined: 26 Feb 2016
Posts: 3386
Location: India
GPA: 3.12
Re: In the figure above, x = y/2, and z = 3y/8. What is the degree measure  [#permalink]

### Show Tags 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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You've got what it takes, but it will take everything you've got 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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# In the figure above, x = y/2, and z = 3y/8. What is the degree measure

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