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In the figure above, having values for which of the following expres
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22 Dec 2022, 10:21
22 Dec 2022, 10:21
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50% (01:42) correct
50% (01:10) wrong based on 12 sessions
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In the figure above, having values for which of the following expressions individually would be sufficient to solve for the value of r?
Indicate all such values.
A. q
B. s
C. t
D. u
E. v
F. s+u
G. u+v
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Official Answer
A,B,C,G
Re: In the figure above, having values for which of the following expres
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04 Jan 2023, 03:34
04 Jan 2023, 03:34
Expert Reply
OE
Because s, u, and v are the interior angles of a triangle, s + u+ v = 180. Also, since r and s are supplementary angles, r + s = 180. Therefore, s + u+ v = r + s, which implies that u + v = r. So knowing the value of u + v would enable you to solve for r. Thus, choice (G) is correct. Knowing u or 1; individually would not enable you to solve for r, nor would knowing the sum s + u. (That sum would enable you to solve for v, which you have already established is not sufficient to solve for r.)
As previously stated, r + s = 180, so knowing s would enable you to solve for r. Thus, choice (C) is correct. Finally, q and s are opposite angles, as are r and t, so q = s and r=t. Thus, knowing t gives you r directly, and knowing q gives you s directly, which were already demonstrated to be sufficient. Thus, choices (A) and (B) are correct.
Because s, u, and v are the interior angles of a triangle, s + u+ v = 180. Also, since r and s are supplementary angles, r + s = 180. Therefore, s + u+ v = r + s, which implies that u + v = r. So knowing the value of u + v would enable you to solve for r. Thus, choice (G) is correct. Knowing u or 1; individually would not enable you to solve for r, nor would knowing the sum s + u. (That sum would enable you to solve for v, which you have already established is not sufficient to solve for r.)
As previously stated, r + s = 180, so knowing s would enable you to solve for r. Thus, choice (C) is correct. Finally, q and s are opposite angles, as are r and t, so q = s and r=t. Thus, knowing t gives you r directly, and knowing q gives you s directly, which were already demonstrated to be sufficient. Thus, choices (A) and (B) are correct.
gmatclubot
Re: In the figure above, having values for which of the following expres [#permalink]
04 Jan 2023, 03:34
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