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Sub 505 (Easy)|   Geometry|      
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Bunuel
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In the figure below, what is the value of xº? 21 Jun 2021, 01:30
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E
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In the figure below, what is the value of xº?

A. 20º
B. 35º
C. 70º
D. 110º
E. 145º


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E
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In the figure below, what is the value of xº? 21 Jun 2021, 03:33
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Angle DEA = 110
Angle EDA = 35
Angle X = 180- 35 = 145

E is the answer IMO

Bunuel

In the figure below, what is the value of xº?

A. 20º
B. 35º
C. 70º
D. 110º
E. 145º


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In the figure below, what is the value of xº? 21 Jun 2021, 03:43
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AEB + 90 + 20 = 180 (Triangle sum property)
AEB = 70

DEA + AEB = 180
DEA = 110

In triangle DEA, ED=EA (isosceles triangle)
110 + 2x =180
EDA = 35
CDB = 180 - 35 = 145

IMO E
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In the figure below, what is the value of xº? 21 Jun 2021, 08:54
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, Answer must be E. 145º
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In the figure below, what is the value of xº? 21 Jun 2021, 11:02
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Angle AEB = 90- 20 = 70
Angle AED = 180 - 70 = 110

So, angle EDA = angle EAD = 70/2 = 35

And x = 180 - 35 = 145. So, I think E. :)
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In the figure below, what is the value of xº? Updated on: 21 Jun 2021, 11:38
Originally posted by CrackverbalGMAT on 21 Jun 2021, 11:38.
Last edited by CrackverbalGMAT on 21 Jun 2021, 11:38, edited 1 time in total.
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Solution:

In triangle AEB, the angle DEA = 90+20=110 degrees (In a triangle, External angle = Sum of internal opposite angles)

Thus angle EDA =EAD =180-110 / 2 = 35 degrees

=>DAB =90 + 35 =125 degrees

=> x = 125 + 20 =145 degrees (In a triangle, External angle = Sum of internal opposite angles) (option e)

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In the figure below, what is the value of xº? 21 Jun 2021, 11:38
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Bunuel

In the figure below, what is the value of xº?

A. 20º
B. 35º
C. 70º
D. 110º
E. 145º


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∠AEB + 90 + 20 = 180
∠AEB = 70

∠DEA + ∠AEB = 180
∠DEA = ∠110

In triangle DEA:
110 + 2x =180
2x = 70
x = 35. So, ∠EDA = ∠DAE = 35
∠CDB = 180 - 35 = 145. IMO, (E)!
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