GeminiHeat wrote:
The figure above shows two lines intersecting at the point O. If the lines are rotated about O at the same rate and in the directions shown until
AB⊥CD, through how many degrees must each line move?
A.
90−θB.
90−θ2C.
90+θ2D.
90+θ2E.
90+2θ2These kinds of questions (Variables in the Answer Choices - VIACs) can be answered algebraically or using the INPUT-OUTPUT approach.
The two posters above have solved the question algebraically, so let's use the INPUT-OUTPUT approach.
Let the ORIGINAL angle =
40°If we keep rotating the lines....
..... we'll eventually get to the point where the angle of intersection =
0°At this point, the two lines have rotated a total of
40°From here, we keep rotating the lines....
..... until the angle of intersection is
90°At this point, the two lines have rotated an additional
90° (starting from when the angle of intersection was
0°)
40° +
90° =
130°So, the TWO lines have rotated a total of
130°This means EACH line rotates
65°So, when we INPUT a starting angle of
40°, the answer to the question (aka the OUTPUT) =
65°At this point we check each answer choices to see which one yields and output of
65 when we input a starting value
θ =
40A.
90−40= 50. NO GOOD. We want an output of
65B.
90−402= 70. NO GOOD. We want an output of
65C.
90+402 110. NO GOOD. We want an output of
65D.
90+402 65. GREAT!
E.
90+2(40)2 85. NO GOOD. We want an output of
65Answer: D
Cheers,
Brent
23 Nov 2021, 07:07 
55% (02:10) correct
