求助一道几何题?????

scorpio2rd

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

我怎么决的是C呀... 因为内角和=360.

如果知道两个角是90. ABC = 2BCD.一定是ABC = 90 (反之就是180+90+90+X = 360, 不可能出现),两个90+ 45, 就可以知道最后的那个角是不等于60的...所以就成立呀....那里错了吗?

nils

讨论ABC 若ABC=90 则 BCD=45， 剩下两个一个90一个135 这种情况你讨论了

但是还有可能 ABC和BCD都不是90，CDA和DAB是90. 这时ABC=120，BCD=60

所以条件1+2仍然无法判断是否存在60度的内角