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What is the measure, in degrees, of angle BCA in quadrilateral ABCD?

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What is the measure, in degrees, of angle BCA in quadrilateral ABCD?  [#permalink]

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New post 21 Nov 2016, 12:00
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What is the measure, in degrees, of angle BCA in quadrilateral ABCD?

(I) ABCD is a trapezoid with AD parallel to BC

(II) The measure of CAD angle is 35 degrees

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Re: What is the measure, in degrees, of angle BCA in quadrilateral ABCD?  [#permalink]

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New post 21 Nov 2016, 12:40
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Is the answer (C) -> Both statements are required.

If we know both sides are parallel then angle CAD = angle BCA = 35 degrees.
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What is the measure, in degrees, of angle BCA in the quadrilateral ABC  [#permalink]

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New post 30 Nov 2016, 07:23
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What is the measure, in degrees, of angle BCA in the quadrilateral ABCD?

(I) ABCD is a trapezoid with AD and BC parallels
(II) The measure of angle CAD is 35º
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Re: What is the measure, in degrees, of angle BCA in the quadrilateral ABC  [#permalink]

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New post 30 Nov 2016, 11:44
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Hi Felippemed,

Whenever you have parallel lines always look for a transversal. A transversal is a line cutting two parallel lines. The transversal will always give you alternate angles which are equal and corresponding angles which are also equal. If in a question lines are given to be parallel always look for alternate and corresponding angles.

The question here asks us to find the measure of angle BCA.

Statement 1 : ABCD is a trapezoid with AD and BC parallels

We just know that AD and BC are parallel. We have no information about the angles. Insufficient.

Statement 2 : The measure of angle CAD is 35º

We just have the measure of CAD, we cannot infer any information about the other angles. Insufficient.
There is a good chance that some people mark this statement sufficient. The trap laid here is for us to take information from the first statement and use it with the second. Remember in a DS question we need to check the statements individually first. We should shy away from using information given in the first statement with the second while evaluating them individually.

Combining 1 and 2

AD and BC are parallel and angle CAD is 35 degrees. Since angles BCA and CAD are alternate, angle BCA will also be 35 degrees.

OA : C

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Re: What is the measure, in degrees, of angle BCA in the quadrilateral ABC  [#permalink]

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New post 30 Nov 2016, 12:20
felippemed wrote:
What is the measure, in degrees, of angle BCA in the quadrilateral ABCD?

(I) ABCD is a trapezoid with AD and BC parallels
(II) The measure of angle CAD is 35º


FROM STATEMENT - I ( INSUFFICIENT )

Value of ∠s is not given so, we can not find the value of ∠BCA.

FROM STATEMENT - II ( INSUFFICIENT )

We are given only the value of ∠CAD , which is insufficient to calculate the value of ∠BCA.

FROM STATEMENT - I & II ( SUFFICIENT )

Since we know that AD || BC , and the value of ∠CAD we can find the value of alternate ∠BCA.

Thus, BOTH statements (1) and (2) TOGETHER are sufficient to answer the question asked, but NEITHER statement ALONE is sufficient to answer the question asked, answer will be option (C)
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Re: What is the measure, in degrees, of angle BCA in the quadrilateral ABC  [#permalink]

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New post 01 Dec 2016, 04:12
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The question is based on simple property of parallel lines.
Option 1: Both lines are parallel. But we don't know value of the angle CAD. Hence not possible to determine the answer - Insufficient
Option 2: Only measure of angle has given, i.e. CAD is 35. However, It is not possible to determine the answer as we don't know about the two lines AD and BC.

Together, As both the lines AD and BC parallel and angle CAD is known. Angle BCA can be determined.
Angle CAD = Angle BCA = 35. Answer is C.
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Re: What is the measure, in degrees, of angle BCA in quadrilateral ABCD?  [#permalink]

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New post 02 Dec 2016, 08:15
I think that what one has to take from this question is that parallel structure doesn't mean a isosceles trapezoid, and a "irregular trapezoid" still allow you to find some info.

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Re: What is the measure, in degrees, of angle BCA in quadrilateral ABCD?  [#permalink]

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Re: What is the measure, in degrees, of angle BCA in quadrilateral ABCD?   [#permalink] 23 Nov 2019, 07:45
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