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Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees? (1) Two of the interior angles of ABCD are right angles. (2) The degree measure of angle ABC is twice the degree measure of angle BCD.

A. Statement (1) ALONEis sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONEis sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHERare sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.

My approach to the problem :

Each statement individually cannot help solve the question. Using combined information from two statements:

It isn't clear from combined information whether angle BCD is right angle. So two cases arises here.

Case 1: If angle BCD is not the a right angle. In this case Angle ABC is 60 degrees since ABC + BCD = 180 degress as sum of other two angles of quadrilateral is 180 degress.

Case 2: If angle BCD is the right angle. In this case angle ABC is 45 degrees and other angles of quadrilateral are 90 and 135 degrees.

So we cannot clearly say that angle ABC is 60 with both information combined and so my answer to this is E but the official answer is otherwise.

Is the measure of one of the interior angles of quadrilateral ABCD equal to 60 degrees? (1) Two of the interior angles of ABCD are right angles. (2) The degree measure of angle ABC is twice the degree measure of angle BCD.

A. Statement (1) ALONEis sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONEis sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHERare sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.

My approach to the problem :

Each statement individually cannot help solve the question. Using combined information from two statements:

It isn't clear from combined information whether angle BCD is right angle. So two cases arises here.

Case 1: If angle BCD is not the a right angle. In this case Angle ABC is 60 degrees since ABC + BCD = 180 degress as sum of other two angles of quadrilateral is 180 degress.

Case 2: If angle BCD is the right angle. In this case angle ABC is 45 degrees and other angles of quadrilateral are 90 and 135 degrees.

So we cannot clearly say that angle ABC is 60 with both information combined and so my answer to this is E but the official answer is otherwise.

Please correct if my logic is incorrect.

Merging similar topics. please refer to the solution above.

Re: Is the measure of one of the interior angles of [#permalink]
06 Oct 2012, 05:30

Since two angles of the quad. are right angles, would other angles not be right angles as well? As sides emanating from right angles would only be straight, and hence the corresponding angles will also be right angles? Correct me if I am wrong. Thx.

Re: Is the measure of one of the interior angles of [#permalink]
06 Oct 2012, 05:49

Expert's post

chigiwigi wrote:

Since two angles of the quad. are right angles, would other angles not be right angles as well? As sides emanating from right angles would only be straight, and hence the corresponding angles will also be right angles? Correct me if I am wrong. Thx.

Consider the diagram below:

Attachment:

Trapezoid.png [ 1.62 KiB | Viewed 2353 times ]

As you can see we can have a quadrilateral with only two right angles.

Re: Is the measure of one of the interior angles of [#permalink]
28 Jul 2014, 07:52

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