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 1530 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!\)