Skip to main content

2007 AMC 12B Problem 11

Problem 11 of 25IntermediateGeometryArithmetic

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

Answer choices

Show solution

Solution

Let x=∠A.x=\angle A. Then ∠B=x2,\angle B=\tfrac x2, ∠C=x3,\angle C=\tfrac x3, and ∠D=x4.\angle D=\tfrac x4. The angle sum gives x+x2+x3+x4=25x12=360, x+\dfrac x2+\dfrac x3+\dfrac x4=\dfrac{25x}{12}=360, so x=12⋅36025=172.8≈173.x=\dfrac{12\cdot360}{25}=172.8\approx173. Thus, the correct answer is D.
AoPS wiki

Tagged: angle sum · ratio and proportion

More practice