Problem

1970 AHSME Problem 30

[asy] size(175); defaultpen(linewidth(0.8)); real r=50, a=4,b=2.5,c=6.25; pair A=origin,B=c*dir(r),D=(a,0),C=shift(b*dir(r))*D; draw(A--B--C--D--cycle); label("$A$",A,SW); label("$B$",B,N); label("$C$",C,E); label("$D$",D,S); label("$a$",D/2,N); label("$b$",(C+D)/2,NW); [/asy]

In the accompanying figure, segments $AB$ and $CD$ are parallel, the measure of $\angle{D}$ is twice the measure of $\angle{B}$ , and the measures of segments $AB$ and $CD$ are $a$ and $b$ respectively. Then the measure of $AB$ is equal to

$\textbf{(A) }\dfrac{1}{2}a+2b\qquad \textbf{(B) }\dfrac{3}{2}b+\dfrac{3}{4}a\qquad \textbf{(C) }2a-b\qquad \textbf{(D) }4b-\frac{1}{2}a\qquad \textbf{(E) }a+b$

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.

Show/Hide Problem Tags

Problem Tags: No tags

Want to contribute problems and receive full credit? Click here to add your problem!
Please report any issues to us in our Discord server
Go to previous contest problem (SHIFT + Left Arrow) Go to next contest problem (SHIFT + Right Arrow)

Problem feedback

Difficulty —

Category: AHSME
Points: 3
Back to practice
Train more like this