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805+ (Hard)|   Geometry|      
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lucajava
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In the figure shown below, what is the value of angle α? 21 Apr 2019, 15:39
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C
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

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95% (hard)

Question Stats:

28% (02:22) correct 72% (02:41) wrong based on 29 sessions

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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
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C
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PKN
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In the figure shown below, what is the value of angle α? 21 Apr 2019, 18:44
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lucajava
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
Show more

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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GMAT Focus 1: 735 Q90 V89 DI81
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In the figure shown below, what is the value of angle α? 21 Apr 2019, 19:13
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lucajava
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
Show more


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
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jfranciscocuencag
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In the figure shown below, what is the value of angle α? 06 May 2019, 18:43
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PKN
lucajava
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

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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Hello PKN!!!

How do we know that is isosceles?

Kind regards!
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PKN
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In the figure shown below, what is the value of angle α? 07 May 2019, 02:21
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Hi jfranciscocuencag,

Please refer the diagram attached with my original explanation:

1) In the triangle ABC, Angle BAC=180-(60+20)-50=50 degree=Angle BCA

Hence, AB=BC------------(1)

2) In the triangle DBC, Angle BDC=180-60-(50+10)=60 degree=Angle BCD

Hence, BC=BD------------(2)

Now, from(1) and (2) , we have AB=BD.

Hope it helps.
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In the figure shown below, what is the value of angle α? 11 Jun 2025, 01:26
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