LakerFan24 wrote:
In the figure attached, DE is parallel to FG and DG = EF. What is the value of x+y?
A) 180
B) 220
C) 240
D) 300
E) 360
Nice solutions, here . . .
But you don't need to draw a triangle.
The key is that
DG = EFIt's an
isosceles trapezoid.
You can derive y or z, and hence x, from the following
properties (see diagram):
A - The lower base angles are congruent (here, G and F)
B - The upper base angles are congruent (here, D and E) - I didn't use this one, but if you were looking for angles that summed to 360, it would help quickly
C - Opposite angles are supplementary, i.e., sum to 180 (\(\frac{x}{3}\) and y are supplementary)
D - Adjacent angles are also supplementary (y and z)
Attachment:
ISOCELES TRAPEZOID.jpg [ 19.19 KiB | Viewed 1830 times ]
To answer the question1. Derive z from the straight line. 120 + z = 180,
z = 602. Derive x. Angles G and z are congruent base angles, see C above. Angle G = \(\frac{x}{3}\), so z = \(\frac{x}{3}\) ==>
\(\frac{x}{3}\)= 60,
x = 180.
3. Derive y EITHER
-- from interior angles property, see D above (if z is 60, y will be 120), y = 120 OR
-- from drawing extended lines, see diagram (120 and y are alternate interior angles of parallel lines cut by a transversal),
y = 120Solutiony = 120
x = 180
x+y = 300 Answer D
Hope that helps.
\(
Note to self: READ the question. I didn't catch DG=EF until more than three minutes in, AND I didn't catch "x + y" and marked the wrong answer.
Edited to add figure, edited again to simplify post!\)
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