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16 Mar 2022, 07:15
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D
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Difficulty:
45%
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Question Stats:
63% (02:06) correct
37%
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A and B are the endpoints of a line segment. Segment AB is crossed through point C by another line segment with endpoints D and E. If ∠ACD > 90?, and the sum of ∠ACE and ∠BCD is x, then which of the following must be true?
A. x < 90
B. x > 90
C. 90 < x < 180
D. x < 180
E. x > 180
Are You Up For the Challenge: 700 Level Questions
A. x < 90
B. x > 90
C. 90 < x < 180
D. x < 180
E. x > 180
Are You Up For the Challenge: 700 Level Questions
16 Mar 2022, 23:25
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Ans will be B
since in the below diagram c is the point of intersection. If ∠ACD > 90 which means ∠BCD is less than 90 because the angle of a straight line is 180 degrees. for eg. if ∠ACD is 110 degrees then ∠BCD is max 70 degrees.
since in the below diagram c is the point of intersection. If ∠ACD > 90 which means ∠BCD is less than 90 because the angle of a straight line is 180 degrees. for eg. if ∠ACD is 110 degrees then ∠BCD is max 70 degrees.
17 Mar 2022, 00:02
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∠ACD = ∠ECB (Opposite angles)
∠ACE = ∠BCD (Opposite angles)
Total angle around a point = 360
Let ∠ACD = ∠ECB = a
∠ACE + ∠BCD = x
2a+x = 360
We can test the minimum and maximum values for a to get the range
Minimum a = 91
2*91 + x = 360
x = 360-182 = 178
Maximum a = 179
2*179+x = 360
358+x = 360
x = 360-358 = 2
X<180
Answer D
∠ACE = ∠BCD (Opposite angles)
Total angle around a point = 360
Let ∠ACD = ∠ECB = a
∠ACE + ∠BCD = x
2a+x = 360
We can test the minimum and maximum values for a to get the range
Minimum a = 91
2*91 + x = 360
x = 360-182 = 178
Maximum a = 179
2*179+x = 360
358+x = 360
x = 360-358 = 2
X<180
Answer D
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