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The figure shows that line m is parallel to the line n, and l is paral

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MathRevolution
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The figure shows that line m is parallel to the line n, and l is paral [#permalink] New post   14 Oct 2019, 00:31
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[GMAT math practice question]

The figure shows that line \(m\) is parallel to the line \(n\), and \(l\) is parallel to \(k\). Moreover, \(∠CBD=45^o, ∠FAE=80^o.\) What is \(∠BDC\)?

Attachment:
10.14ps.png
10.14ps.png [ 19.74 KiB | Viewed 1778 times ]


\(A. 40^o\)

\(B. 45^o\)

\(C. 50^o\)

\(D. 55^o\)

\(E. 60^o\)
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D
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Re: The figure shows that line m is parallel to the line n, and l is paral [#permalink] New post   14 Oct 2019, 01:30
Angle at BAD =80°

Since ABCD is a parallelogram
Opp angles are equal and sum of angles is 360°

So angle ADC will be 100°

Angle CBD = Angle ADB =45°

So angle BDC will be 100-45= 55°

OA:D

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Re: The figure shows that line m is parallel to the line n, and l is paral [#permalink] New post   14 Oct 2019, 20:40
As m and n & k and l are parallel, ABCD is a parallelogram.
As ABCD is //, it's two opposite angles are same.
<EAF =80°, then<DAB is also 80°, as both are vertically opposite of the two straight lines.
It implies that <DCB =80°.
Triangle DCB, CBD+BCD+BDC= 180
80+45+BDC=180
BDC =55.
Hence, D.
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Re: The figure shows that line m is parallel to the line n, and l is paral [#permalink] New post   14 Oct 2019, 21:17
MathRevolution wrote:
[GMAT math practice question]

The figure shows that line \(m\) is parallel to the line \(n\), and \(l\) is parallel to \(k\). Moreover, \(∠CBD=45^o, ∠FAE=80^o.\) What is \(∠BDC\)?

Attachment:
10.14ps.png


\(A. 40^o\)

\(B. 45^o\)

\(C. 50^o\)

\(D. 55^o\)

\(E. 60^o\)

Angle DAB=80 (vertically opposite angle)

Angle DAB + ABC = 180 ( Sum is supplementary)
Angle ABC = 100
Angle ABC = Angle ABD + DBC
Therefore, Angle ABD = 100- 45 = 55

Angle ABD = Angle BDC = 55 ( Alternate interior angles)

D is correct
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Re: The figure shows that line m is parallel to the line n, and l is paral [#permalink] New post   16 Oct 2019, 02:53
Expert Reply
=>

Attachment:
10.14ds(a).png
10.14ds(a).png [ 19.12 KiB | Viewed 1551 times ]


Since lines \(m\) and \(n\) are parallel, we have \(<FBG=<FAE=80°\) and \(80°+<ABD+45°=180°.\)

Then we have \(125°+<ABD=180°\) and \(<ABD=55°\).

Since \(<ABD\) and \(<BDC\) are alternate interior angles, they are congruent and \(<BDC=55°.\)

Therefore, D is the answer.
Answer: D
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Re: The figure shows that line m is parallel to the line n, and l is paral [#permalink] New post   31 Mar 2020, 10:33
MathRevolution wrote:
[GMAT math practice question]

The figure shows that line \(m\) is parallel to the line \(n\), and \(l\) is parallel to \(k\). Moreover, \(∠CBD=45^o, ∠FAE=80^o.\) What is \(∠BDC\)?

Attachment:
10.14ps.png


\(A. 40^o\)

\(B. 45^o\)

\(C. 50^o\)

\(D. 55^o\)

\(E. 60^o\)


Angle BCD = Angle BAD = Angle FAE = 80

Let angle BDC be x

In triangle BCD
80 + 45 + x = 180
x = 55

IMO D
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Re: The figure shows that line m is parallel to the line n, and l is paral [#permalink]
31 Mar 2020, 10:33
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