2007 AMC 10B Problem 15

Problem 15 of 25IntermediateAlgebra Geometry

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?

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Solution

Let

x=\angle A.

Then

\angle B=\dfrac{x}{2},

\angle C=\dfrac{x}{3},

and

\angle D=\dfrac{x}{4}.

The angles sum to

360^\circ,

x+\dfrac{x}{2}+\dfrac{x}{3}+\dfrac{x}{4}=\dfrac{25x}{12}=360.

Thus

x=\dfrac{12\cdot 360}{25}=172.8\approx 173.

Thus, the correct answer is D.