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04 Apr 2021, 11:44
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A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
32% (02:33) correct
68%
(02:38)
wrong
based on 41
sessions
History
Date
Time
Result
Not Attempted Yet
In the figure shown above, line m and n is the bisector of angle ABD and ACE, respectively. z=?
(1) x=70
(2) x=y
(1) x=70
(2) x=y
Attachments
Untitled.jpg [ 18.56 KiB | Viewed 1407 times ]
05 Apr 2021, 23:04
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akshayuberoi
Take angle ABD and ACE as b and a, and mark on the sketch.
\(\triangle ABC\) : The interior angles will be 180-2b and 180-2a respectively. Thus the third angle = x= 180-(180-2b+180-2a)=2a+2b-180
\(\triangle ZBC\) : The interior angles will be b and a respectively, as they are opposite angles to b and a. Thus the third angle = z= 180-(a+b)
\(x=2a+2b-180.......(i)\)
\(z= 180-(a+b).......(ii)\)
Multiply (ii) by 2
\(z= 360-(2a+2b).......(ii)\)
Add this to (i)
\(x+z=2a+2b-180+360-2a-2b=180\)
So we require to know the value of x to know z.
(1) x=70
x+z=180.....z=180-70=110
Sufficient
(2) x=y
Nothing about value of x or y.
Insufficient
A
Attachments
Untitled1111 (2).jpg [ 9.79 KiB | Viewed 1228 times ]
06 Apr 2021, 19:27
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akshayuberoi
See the labled graph below, \(\angle ABD = 180 - y\) and \(\angle ACE = x + y\), split those in half and transpose to the bottom triangle. Then \(\angle BFC\) is \(180 - (\frac{180 - y}{2}) - \frac{x + y}{2} = 90 - \frac{x}{2}\). Thus we only need to know x.
Statement 1:
Sufficient.
Statement 2:
Insufficient.
Ans: A
Attachments
Intersection.png [ 35.39 KiB | Viewed 1167 times ]
