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21 Apr 2019, 15:39
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C
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Difficulty:
95%
(hard)
Question Stats:
28% (02:22) correct
72%
(02:41)
wrong
based on 29
sessions
History
Date
Time
Result
Not Attempted Yet
In the figure shown below, what is the value of angle \(α\)?
A. 70°
B. 75°
C. 80°
D. 90°
E. The given information is not sufficient to answer this question
A. 70°
B. 75°
C. 80°
D. 90°
E. The given information is not sufficient to answer this question
21 Apr 2019, 18:44
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lucajava
Please refer the enclosed diagram,
1) Sides AB=BD=BC=CD
2) Angle AOD=Angle BOC=70°
Now, in the triangle AOD, we have
a) \(α\)+Angle OAD=70°
b) In the triangle ABD, 20°+ \(α\)+ Angle OAD + 50°=180° Or, \(α\)+ Angle OAD=110°
By solving (a) and (b) we have, \(α\)=80°
Ans. (C)
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Picture.png [ 44.02 KiB | Viewed 3689 times ]
21 Apr 2019, 19:13
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lucajava
STEP I : Take triangle ADC.
Angle DAC = 180-D-C=180-(20+60)-50=50, so ADC is isosceles and AD=CD.
STEP II : Take triangle BDC.
Angle DBC = 180-D-C=180-60-(50+10)=60, so BDC is equilateral triangle and BD=CD=BD.
STEP III : Compare AD and BD
Ad=CD and BD=CD, so AD=BD.
STEP IV : Take triangle ADB.
So ADB is isosceles as AD=BD.
Thus angle \(α\)=\(\angle{DAB}=\frac{180-20}{2}=80\)
C
Attachments
000000.png [ 43.07 KiB | Viewed 3594 times ]
