Pls help on GMAT Prep Q
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Source: Beat The GMAT — Data Sufficiency |
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gautamberry
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here it goes..
Angle R=90-T
Angle T=90-R
In triangle RQS
Since triangle RQS is isosceles angle Q= angle S (say A)
R+Q+S=180
90-T+2A=180
A=(90+T)/2
In triangle TSU
Since triangle TSU is isosceles angle U= angle S (say B)
T+S+U=180
90-R+2B=180
B=(90+R)/2
Now for line RST
angle RSQ + angle QSU + angle TSU = 180
A+X+B=180
(90+T)/2 + X + (90+R)/2 = 180
(90+T+2X+90+R)/2 = 180
(180+90+2X)/2 = 180 (Since angle R + angle T + 90 = 180 .....the triangle RPT)
(270+2X)/2 = 180
135+X = 180
X = 45
Hence the answer is C
Hope you got it!!!!
Angle R=90-T
Angle T=90-R
In triangle RQS
Since triangle RQS is isosceles angle Q= angle S (say A)
R+Q+S=180
90-T+2A=180
A=(90+T)/2
In triangle TSU
Since triangle TSU is isosceles angle U= angle S (say B)
T+S+U=180
90-R+2B=180
B=(90+R)/2
Now for line RST
angle RSQ + angle QSU + angle TSU = 180
A+X+B=180
(90+T)/2 + X + (90+R)/2 = 180
(90+T+2X+90+R)/2 = 180
(180+90+2X)/2 = 180 (Since angle R + angle T + 90 = 180 .....the triangle RPT)
(270+2X)/2 = 180
135+X = 180
X = 45
Hence the answer is C
Hope you got it!!!!
orgautamberry wrote:here it goes..
Angle R=90-T
Angle T=90-R
In triangle RQS
Since triangle RQS is isosceles angle Q= angle S (say A)
R+Q+S=180
90-T+2A=180
A=(90+T)/2
In triangle TSU
Since triangle TSU is isosceles angle U= angle S (say B)
T+S+U=180
90-R+2B=180
B=(90+R)/2
Now for line RST
angle RSQ + angle QSU + angle TSU = 180
A+X+B=180
(90+T)/2 + X + (90+R)/2 = 180
(90+T+2X+90+R)/2 = 180
(180+90+2X)/2 = 180 (Since angle R + angle T + 90 = 180 .....the triangle RPT)
(270+2X)/2 = 180
135+X = 180
X = 45
Hence the answer is C
Hope you got it!!!!
B+x = A + R R=90-T
=> B + x = A + 90-T
and A + x = B + T
adding both we have
A+B+2x = A+B+90
therefore, 2x=90 or x=45
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LSB
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What's the rule behindarvindm07 wrote:orgautamberry wrote:here it goes..
Angle R=90-T
Angle T=90-R
In triangle RQS
Since triangle RQS is isosceles angle Q= angle S (say A)
R+Q+S=180
90-T+2A=180
A=(90+T)/2
In triangle TSU
Since triangle TSU is isosceles angle U= angle S (say B)
T+S+U=180
90-R+2B=180
B=(90+R)/2
Now for line RST
angle RSQ + angle QSU + angle TSU = 180
A+X+B=180
(90+T)/2 + X + (90+R)/2 = 180
(90+T+2X+90+R)/2 = 180
(180+90+2X)/2 = 180 (Since angle R + angle T + 90 = 180 .....the triangle RPT)
(270+2X)/2 = 180
135+X = 180
X = 45
Hence the answer is C
Hope you got it!!!!
B+x = A + R R=90-T
=> B + x = A + 90-T
and A + x = B + T
adding both we have
A+B+2x = A+B+90
therefore, 2x=90 or x=45
B+x = A + R
Exterior angle of a triangle is equal to the sum of the opposite interior angles.LSB wrote:What's the rule behindarvindm07 wrote:orgautamberry wrote:here it goes..
Angle R=90-T
Angle T=90-R
In triangle RQS
Since triangle RQS is isosceles angle Q= angle S (say A)
R+Q+S=180
90-T+2A=180
A=(90+T)/2
In triangle TSU
Since triangle TSU is isosceles angle U= angle S (say B)
T+S+U=180
90-R+2B=180
B=(90+R)/2
Now for line RST
angle RSQ + angle QSU + angle TSU = 180
A+X+B=180
(90+T)/2 + X + (90+R)/2 = 180
(90+T+2X+90+R)/2 = 180
(180+90+2X)/2 = 180 (Since angle R + angle T + 90 = 180 .....the triangle RPT)
(270+2X)/2 = 180
135+X = 180
X = 45
Hence the answer is C
Hope you got it!!!!
B+x = A + R R=90-T
=> B + x = A + 90-T
and A + x = B + T
adding both we have
A+B+2x = A+B+90
therefore, 2x=90 or x=45
B+x = A + R
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rabab
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1 says- QR = RS
hence angle RQS = angle RSQ, let angle RQS = angle RSQ = y.
in triangle RQS,
y + y + angle QRS = 180 degree
-> angle QRS = 180 degree - 2y ---- eqn i
now, from 2 we get,
ST = TU
-> angle SUT = angle STU. let angle SUT = angle STU = z
in triangle STU
z + z + angle STU = 180 degree
-> angle STU = 180 - 2z --- eqn ii
now, in triangle RPT,
angle RTP + angle STU + angle PRS = 180 degree
-> 90 degree + (180 - 2z) + (180 degree - 2y) = 180 degree ( solved from eqn i & ii)
-> y+ z = 136 degree -- eqn iii
now,
angle x + angle y + angle z = 180 degree
-> angle x = 180 - 135 (solved from eqn iii)
therefore angle x = 45 degree.
hope it helps
hence angle RQS = angle RSQ, let angle RQS = angle RSQ = y.
in triangle RQS,
y + y + angle QRS = 180 degree
-> angle QRS = 180 degree - 2y ---- eqn i
now, from 2 we get,
ST = TU
-> angle SUT = angle STU. let angle SUT = angle STU = z
in triangle STU
z + z + angle STU = 180 degree
-> angle STU = 180 - 2z --- eqn ii
now, in triangle RPT,
angle RTP + angle STU + angle PRS = 180 degree
-> 90 degree + (180 - 2z) + (180 degree - 2y) = 180 degree ( solved from eqn i & ii)
-> y+ z = 136 degree -- eqn iii
now,
angle x + angle y + angle z = 180 degree
-> angle x = 180 - 135 (solved from eqn iii)
therefore angle x = 45 degree.
hope it helps
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mjjking
- Master | Next Rank: 500 Posts
- Posts: 353
- Joined: Sat Jan 20, 2007 1:29 am
- Location: Italy
- Thanked: 7 times
- GMAT Score:720
While the angle is 90-T and not 180-90-T??!
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