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Is the measure of one of the interior angles of

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Is the measure of one of the interior angles of [#permalink] New post 26 Oct 2005, 21:57
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.
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 [#permalink] New post 26 Oct 2005, 22:04
I go for E.

(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.

Even when we consider (1) and (2) at the same time, there are two possibilities
a) 120 = 60 * 2 (90, 90, 60, 120)
b) 90 = 45 * 2 (90, 90, 45, 135)
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 [#permalink] New post 27 Oct 2005, 10:48
I got C. Can someone explain why that is wrong.

Since the sum of the interior angles is 360, if 1) and 2) are taken together,

a) 120 = 60 * 2 (90, 90, 60, 120)
b) 90 = 45 * 2 (90, 90, 45, 135) <---- does not add up to 360!

so there can only be the 90,90,60,120....
I may be wrong, please explain..

Thanks
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 [#permalink] New post 27 Oct 2005, 10:54
Quote:
b) 90 = 45 * 2 (90, 90, 45, 135) <---- does not add up to 360!


180 + 135 + 45 does add up to 360. Try it on a calculator.
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 [#permalink] New post 27 Oct 2005, 11:13
lol yes it does... sorry
  [#permalink] 27 Oct 2005, 11:13
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