In the \(xy-\)plane above, is angle \(BAC\) greater than

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Princeton Review



In the \(xy-\)plane above, is angle \(BCA\) greater than \(90\) degrees?

1) Points \(A\) and \(B\) have different \(x-\)coordinates.
2) The measure of angle \(B\)is twice the measure angle \(C\).

OA E

[Ian Stewart]

Princeton Review



In the \(xy-\)plane above, is angle \(BCA\) greater than \(90\) degrees?

1) Points \(A\) and \(B\) have different \(x-\)coordinates.
2) The measure of angle \(B\)is twice the measure angle \(C\).

OA E

They should be clear in Statement 2 what angles they're describing - around a point, there are two different angles you can make, the small angle within the triangle, and the large angle around the outside of the triangle (the one that would sum to 360 with the angle inside the triangle). But as the question above is written, if you assume Statement 2 is describing the angles within the triangle ABC, the answer is B. If angle B is twice angle C, then since the angles in a triangle sum to 180 degrees, angle B must be less than 120 degrees, and angle C must be less than 60 degrees, and we have sufficient information to give a 'no' answer to the question.

Since the provided OA of 'E' didn't make any sense, I googled the question, and there's a typo above: the original version of the question asks "Is angle BAC greater than 90 degrees?" (not "angle BCA"). If that's the question, the answer is indeed E, since using both statements, the angles A, B and C can be, respectively, 120, 40 and 20, say, or they can be 60, 80 and 40, say.