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In the figure above, if AB||CE
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23 Apr 2020, 10:25
23 Apr 2020, 10:25
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Question Stats:
86% (01:35) correct
13% (01:45) wrong based on 23 sessions
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In the figure above, if \(AB||CE\), \(CE = DE\), and \(y = 45\), then \(x =\)
A. 45
B. 60
C. 67.5
D. 112.5
E. 135
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Posts: 6218
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In the figure above, if AB||CE
[#permalink]
23 Apr 2020, 12:44
23 Apr 2020, 12:44
1
Carcass wrote:
In the figure above, if \(AB||CE\), \(CE = DE\), and \(y = 45\), then \(x =\)
A. 45
B. 60
C. 67.5
D. 112.5
E. 135
Given: y = 45 and AB||CE
When a transversal intersects two parallel lines (as shown below), we get several equal angles.
So we also know that ∠ECD = x° .
We get the following
Also given: CE = DE
When we add this information to our diagram, we see that ∆ECD is an isosceles triangle, which means ∠CDE = x°
Since angles in a triangle add to 180°, we can write: 45 + x + x = 180
Simplify: 45 + 2x = 180
Subtract 45 from both sides: 2x = 135
Divide both sides by 2 to get: x = 67.5
Answer: C
Cheers,
Brent
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In the figure above, if AB||CE [#permalink]
23 Apr 2020, 12:44
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