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# What is the measure of angle B?

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Math Expert
Joined: 02 Sep 2009
Posts: 52385
What is the measure of angle B?  [#permalink]

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22 Apr 2015, 02:34
00:00

Difficulty:

65% (hard)

Question Stats:

63% (02:30) correct 37% (02:30) wrong based on 117 sessions

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(NOTE: Figure not drawn to scale)

What is the measure of angle B?

(1) y = 243 – 22x

(2) y = 261 – 24x

Kudos for a correct solution.

Attachment:

Triangle_D.S..png [ 4.71 KiB | Viewed 4027 times ]

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Re: What is the measure of angle B?  [#permalink]

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22 Apr 2015, 03:01
Bunuel wrote:

(NOTE: Figure not drawn to scale)

What is the measure of angle B?

(1) y = 243 – 22x

(2) y = 261 – 24x

Kudos for a correct solution.

Attachment:
Triangle_D.S..png

1) we know that sum of all angles equal to $$180$$ so we can write such equation:
$$x^2+6x+243-22x=180$$
$$x^2-16x+63=0$$
$$x$$ can be equal to $$7$$ or $$9$$
Insufficient

2) we know that sum of all angles equal to $$180$$ so we can write such equation:
$$x^2+6x+261-24x=180$$
$$x^2-18x+81=0$$
$$x$$ can be equal only to $$9$$
Sufficient

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Re: What is the measure of angle B?  [#permalink]

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22 Apr 2015, 09:45
Using statement 1 ,
x^2-16x+63=0 , X=7 or 9 ... angle B will depend value on X. so this statement not enough.

Using statement 2 ,
x^2-18x+81=0 , so X=9 ...This is enogh to know value of angle B.

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Re: What is the measure of angle B?  [#permalink]

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22 Apr 2015, 18:11
What is the measure of angle B?
We know that 6x + x^2 + y = 180
y = 6x + x^2 + 180

(1) y = 243 – 22x
6x + x^2 + 180 = 243 – 22x
x^2− 16x + 63 = 0
x=7 or 9
Insufficient

(2) y = 261 – 24x
6x + x^2 + 180 = 261 – 24x
x^2 − 18x + 81= 0
x=9
Sufficient

Math Expert
Joined: 02 Sep 2009
Posts: 52385
What is the measure of angle B?  [#permalink]

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27 Apr 2015, 01:58
Bunuel wrote:

(NOTE: Figure not drawn to scale)

What is the measure of angle B?

(1) y = 243 – 22x

(2) y = 261 – 24x

Kudos for a correct solution.

Attachment:
Triangle_D.S..png

VERITAS PREP OFFICIAL SOLUTION:

The angles of any triangle add up to 180°, so we can write x^2+6x+y=180. However, we cannot figure out angle B, which measures 6x°, until we turn to the additional premises.

Statement (1) gives y=243–22x. Substituting this equation into our original equation gives x^2+6x+243–22x=180. Standardizing and simplifying, this reduces to x^2–16x+63=0. This quadratic gives two possible values of x. It isn’t really necessary to proceed further, but we’ll point out that it factors as (x–7)(x–9)=0 and x=7 or 9. Angle B could measure either 42° or 54°, so statement (1) standing alone is insufficient.

Statement (2) gives y=261–24x. Substituting this equation into our original equation gives x^2+6x+261–24x=180. Standardizing and simplifying, this reduces to x^2–18x+81=0. Unlike the quadratic from statement (1), however, this quadratic is a common algebraic equation – a perfect square. It factors as (x–9)^2=0, and it has only one solution: x=9. In turn, angle B measures 54°. So statement (2) standing alone is sufficient.

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Re: What is the measure of angle B?  [#permalink]

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19 Apr 2018, 02:16
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Re: What is the measure of angle B? &nbs [#permalink] 19 Apr 2018, 02:16
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