Q13: 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) ALONE is sufficient, but statement (2) alone is not sufficient. B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient. C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient. D. EACH statement ALONE is sufficient. E. Statements (1) and (2) TOGETHER are NOT sufficient.
答案是E,但我觉得是C,哪位好心NN帮我看看,万分感谢!
首先由(1)是得出要么该四边形为长方形(相邻两角为90度)则没有角为60度,要么得出该四边的一对对角为直角,另外两个角度不知,所以由(1)得不出明确的答案。 由(2)知一个角是其相邻的另一个角的2倍,单独也得不出结论。
由(1)(2)共同得知这个四边行有一对相对的角为90度,不可能是长方形了,且四个角里面有一个角是另一个角的两倍。因为是相邻的角,只能是90度角是它旁边的角的两倍,不可能是旁边的角是90度的两倍。从而这个四边形的角分别为90,45,90,135,没有一个是60度。 所以应该选C
帮我看看,谢谢!!! |