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

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

(2) The measure of CAD angle is 35 degrees


st1) AD || BC, so <BCA = <CAD, but we don't know about <CAD so INSUFFICIENT

st2) Simply knowing <CAD doesn't help with calculating <BCA. Hence INSUFFICIENT

st1 and st2 taken together, <BCA = <CAD = 35 SUFFICIENT

So, the answer is C
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From the above figure, we can only conclude that the sum of total angle of all four sides will be 360°.
We need to find the measure of angle BCA. Lets look at the statements individually.

Statement I: ABCD is a trapezoid with AD parallel to BC
We can only conclude that since AD//BC, ∠BCA=∠CAD, but we don't know the specific value for either of the angles. NOT SUFFICIENT Eliminate A,D

Statement II: The measure of CAD angle is 35 degrees
We just know that CAD is 35°, and this information is not sufficient. Eliminate B
Combining I and II.
From I: ∠BCA=∠CAD
From II: ∠CAD= 35°
=> ∠BCA= 35° Sufficient. Option C is the answer
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Answer C.

Statement 1 tells us that angle BCA = angle CAD, but we don't know the measure of the angles.

Statement 2 tells us angle BCA = 35 deg. but we don't know the correlation between the two angles.

Combine: CAD = 35 deg.

Answer C.
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1. Does not tell us anything about the value of any of the angles. Insufficient.
2. Knowing the value of CAD alone does not help us calculate BCA. Insufficient.

Combining both, since lines are parallel, BCA will be same as CAD. Hence C is the right answer.
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Quote:
What is the measure, in degrees, of angle BCA in quadrilateral ABCD?

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

(2) The measure of CAD angle is 35 degrees

(1) insufic

(2) insufic

(1/2) sufic

CAD=BCA=35

(C)
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1) BC parallel to AD; no info about the angles.
Not sufficient

2) Angle CAD is 35 degrees; cant deduce any info.

1+2;
BC parallel to AD; line passing through AC acts as transversal,
Angle CAD = Angle BCA
35 = Angle BCA
Yes, we can answer the Q with certainty

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

(1) ABCD is a trapezoid with AD parallel to BC
By this we will get nothing
Insufficient

(2) The measure of CAD angle is 35 degrees
By this we will not get anything further
Insufficient

Combining 1 and 2

Sufficient
angle BCA=35
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What is the measure, in degrees, of angle BCA in quadrilateral ABCD?

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

(2) The measure of CAD angle is 35 degrees

Statement 1 and 2 separately are not sufficient, but using them together, we can see that the angles situated at the opposite side of two parallel lines will be equal. So, angle BCA will be equal to the angle CAD, which value is given in statement 2.

C is the answer.
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Hi Bunuel,

This question is same as the question I got in GMAT PREP 5. Pls, check if you would like to add a tag for the same.

Thanks!
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Sam2021
Hi Bunuel,

This question is same as the question I got in GMAT PREP 5. Pls, check if you would like to add a tag for the same.

Thanks!

That helps. Added the tag. Thank you!
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