Maybe I'm Stupid, But I Don't Understand This Problem...

Test Preparation ACT Preparation
1

<p>Okay, it's Math problem #39 in the 2009-2010 Preparing for the ACT Booklet provided by the ACT, and frequently passed out by Guidance Counselors. Her's how it goes, word-for-word...</p>

<p>In the figure below, B lies on (line)AC, (line)BD bisects (angle)ABE, and (line)BE bisects (angle)CBD. What is the measure of (angle)DBE? </p>

<p>The diagram looks like a triangle placed between two parallel lines, but there is no indication of the lines being parallel nor is there any indication of any of the angles in the figure. The type of triangle displayed is also not clear, as well.</p>

<p>A. 90 degrees
B. 60 degrees (correct answer)
C. 45 degrees
D. 30 degrees
E. Cannot be deternimed from the given information (which is what I chose)</p>

<p>Basically, the only information given was located in the question wording itself, and not on the diagram. I don't understand how the correct answer can be obtained from only that information.</p>

<p>Any insight would be appreciated.</p>

2

<p>“bisects” is your key, implies same distance on each side</p>

3

<p>Because of the bisecting lines DB and EB, angles ABD = DBE and DBE = CBE. Therefore, The three angles are the same. The angles on the straight line (AC) must add up to 180 degrees, so you take 180/3 = 60 degrees each. Angle DBE = 60 degrees, so the answer is B.</p>

4

<p>^Thanks, y’all.</p>

<p>Didn’t realize that bisecting rule existed (long time since freshman geometry). That basically solves the problem, though.</p>