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If EF is parallel to DG, the length of AB is half of that of AC, the

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If EF is parallel to DG, the length of AB is half of that of AC, the [#permalink]

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CHALLENGE PROBLEM



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If EF is parallel to DG, the length of AB is half of that of AC, the length of CG is equal to that of CD, and the length of DE is equal to that of EF, what is the measure of angle DFE in degrees?

(A) 47.5º
(B) 50º
(C) 52.5º
(D) 55º
(E) 57.5º

[Reveal] Spoiler:
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[Reveal] Spoiler: OA

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If EF is parallel to DG, the length of AB is half of that of AC, the [#permalink]

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New post 17 Oct 2017, 03:52
\(\triangle\) ABC is a right angle triangle where AB=(1/2)BC. The angle split would be 30:60:90 in such a case. \(\angle ACB\)=\(30^{\circ}\) .
moving on to \(\triangle\)CDG which is a isosceles triangle \(\angle\) DCG is =\(30^{\circ}\) by using opposite angles property.
Now the rest of two angles \(\angle\) CDG and \(\angle\) CGD will be \(75^{\circ}\).
since EF is parallel to DG so \(\angle\) DEF is also \(75^{\circ}\).
\(\triangle\) DEF is also an isosceles triangle so \(\angle\) DFE= (180-75)/2=52.5

Last edited by animesh mohanty on 18 Oct 2017, 01:06, edited 1 time in total.

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Re: If EF is parallel to DG, the length of AB is half of that of AC, the [#permalink]

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New post 17 Oct 2017, 08:31
Given that AB=1/2AC. Triangle must be a 30-60-90 right angled triangle.
LACB=30 deg.,therefore LDCG=30 deg.
Since CG=CD, LCGD=LCDG=75 deg.
EF is parallel to DG, therefore LDEF=LCDG= 75 deg.
DE=EF
Therefore in triangle DEF, LE=75 and LEFD=LEDF=(180-75)/2=52.5
Answer C.

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Re: If EF is parallel to DG, the length of AB is half of that of AC, the   [#permalink] 17 Oct 2017, 08:31
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