Is the measure of one of the interior angles of quadrilateral ABCD equ

The diagram shows you two cases using both the statements. In one case, you have a 60 degree angle, in the other case, you don't. Hence both statements together are insufficient.

in statement 1 it has been told us that two of the interior angles are of 180 hence substract 360-180=180 now reaching to second statement. One of the angle is twice the another. in that case i would go with formula
x+2x=180 or 3x=180 hence x=60.

please clariy

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

Hope it helps.

Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

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

In the original condition, there are 4 variables(A,B,C,D) and 1 equation(A+B+C+D=180), which should match with the number of equations. So you need 3 more equations. For 1) 1 equation, for 2) 1 equation, which is likely to make E the answer. When 1) & 2)
Just like the above, there are both yes and no, which is not sufficient. Therefore, the answer is E.


-> For cases where we need 3 more equations, such as original conditions with “3 variables”, or “4 variables and 1 equation”, or “5 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 80% chance that E is the answer (especially about 90% of 2 by 2 questions where there are more than 3 variables), while C has 15% chance. These two are the majority. In case of common mistake type 3,4, the answer may be from A, B or D but there is only 5% chance. Since E is most likely to be the answer using 1) and 2) separately according to DS definition (It saves us time). Obviously there may be cases where the answer is A, B, C or D.

This question is similar to in-the-figure-above-what-is-the-perimeter-of-rectangle-abpq-2821.html in that both are from GMAT Prep and both use the same trap. Check it out! And if you fell for this Q please don't fall for the question in the link. I fell for both

(C) is very tempting, but ignores a tricky possibility. The answer is actually (E).

(1) by itself tells us that the two remaining angles sum to 180, but we have no idea if they're 120/60 or some other combination, so it's insufficient.

(2) just tells us that one angle is twice another. We might have a 60 degree angle, but again we might not, so it's insufficient.

Combined, it's very tempting to say that the angles have to be 90/90/120/60. However, the angles also could be 90/90/45/135, since 90 is twice as much as 45, so statement (2) is still satisfied. Therefore, we may or may not have a 60 degree angle: choose (E).

Target question: Is the measure of one of the interior angles of quadrilateral ABCD equal to 60?

Key concept: the 4 angles in a quadrilateral must add to 360 degrees

Statement 1: Two of the interior angles of ABCD are right angles.
Let's test some possible cases.
There are infinitely many quadrilaterals that satisfy statement 1. Here are two:
Case a: the 4 angles in ABCD are 90°, 90°, 60°, and 120°. In this case, the answer to the target question is YES, one of the angles IS 60°
Case b: the 4 angles in ABCD are 45°, 90°, 90° and 135°. In this case, the answer to the target question is NO, one of the angles is NOT 60°
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: The degree measure of angle ABC is twice the degree measure of angle BCD.
Let's test some possible cases.
Case a: the 4 angles in ABCD are 90°, 90°, 60°, and 120°. In this case, the answer to the target question is YES, one of the angles IS 60°
Case b: the 4 angles in ABCD are 45°, 90°, 90° and 135°. In this case, the answer to the target question is NO, one of the angles is NOT 60°
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
IMPORTANT: Notice that I was able to use the same counter-examples to show that each statement ALONE is not sufficient. So, the same counter-examples will satisfy the two statements COMBINED.
In other words,
Case a: the 4 angles in ABCD are 90°, 90°, 60°, and 120°. In this case, the answer to the target question is YES, one of the angles IS 60°
Case b: the 4 angles in ABCD are 45°, 90°, 90° and 135°. In this case, the answer to the target question is NO, one of the angles is NOT 60°
Since we cannot answer the target question with certainty, the combined statements are NOT SUFFICIENT

Answer: E

Cheers,
Brent

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