2007 AMC 12B Problem 11

Below is the professionally curated solution for Problem 11 of the 2007 AMC 12B, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 12B solutions, or check the answer key.

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Concepts:angle sum ratio and proportion

Difficulty rating: 1270

11.

The angles of quadrilateral $ABCD$ satisfy $\angle A=2\angle B=3\angle C=4\angle D.$ What is the degree measure of $\angle A,$ rounded to the nearest whole number?

$125$

$144$

$153$

$173$

$180$

Solution:

Let $x=\angle A.$ Then $\angle B=\tfrac x2,$ $\angle C=\tfrac x3,$ and $\angle D=\tfrac x4.$

The angle sum gives $x+\dfrac x2+\dfrac x3+\dfrac x4=\dfrac{25x}{12}=360,$ so $x=\dfrac{12\cdot360}{25}=172.8\approx173.$

Thus, the correct answer is D.

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