Geometry-pls help me understand

[email protected] wrote:Hi Experts,


Please help me with the tricks being used in this problem.

Thanks

Since AB is parallel to EH, AG serves as the transversal, and therefore if angle EGC = 70°, angle BAC is also equal to 70°. In triangle ABC, AB = BC, hence BCA also equals 70°.

Also, BD is parallel to FH and with DF serving as transversal, the co-interior angles at D and F are supplementary, in other words, angle at D will be equal to the sum of equal angles FEH and FHE in the isosceles triangle EFH.

Focus on the interior angles in quadrilateral CDEG now, C = G = 70°. Try plugging in the answers from here onward.

(C) If D = 75°, angle at F is 105°, and this will result fractional angle at E. Not fitting, eliminate C and so eliminate all odd numbered choices, A and E also eliminated, as those would result in a fractional angle at E.

Try (D) 80° as (B) 70° sounds like a trap answer. If D = 80°, angle at F is 100°, angles FEH and FHE would equal 40° each, or angle DEG will equal 140°. This satisfies the angle sum property of a quadrilateral; hence [spoiler](D)[/spoiler] is the right answer.

[spoiler]{D}[/spoiler]

Just one clarification are angles ABC and EHF congruent because they are corresponding angles?

[email protected] wrote:HI shibsriz,

When a Quant question includes a bunch of criss-crossing lines and focuses on the various angles within those lines, you should keep the following rules in mind:

1) Lines add up to 180 degrees
2) Opposite angles are equal
3) Parallel lines that are crossed by a third line will create duplicate angles
4) Triangles add up to 180 degrees
5) ANY 4-sided shape adds up to 360 degrees
6) A set of angles that meet at 1 point (and surround that point) will add up to 360 degrees

Drawing the picture and "filling in" the angles you know will help you to figure out the other angles and answer whatever question is asked.

GMAT assassins aren't born, they're made,
Rich

[email protected] wrote:Just one clarification are angles ABC and EHF congruent because they are corresponding angles?

Nope! The angles ABC and EHF are congruent because these are included between two sets of parallel lines. If someone finds it hard to understand this theory, they can always plug in the answer and can still win the battle without any fight.

Reorient the figure as follows:



Since EH || AB, ∠EGC = 70º, and AB=BC, we get:


Since EH || AB and BD || FH, the angles shown below are all 40º:


Since EF = FH, we get:


Since BD || FH, we get the angles shown below:


The correct answer is D.