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If AD = DE and EC = CB as shown above, what is the value of xº?

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Bunuel
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If AD = DE and EC = CB as shown above, what is the value of xº? [#permalink] New post   13 Jul 2021, 01:30
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A
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C
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If AD = DE and EC = CB as shown above, what is the value of xº?

A. 15º
B. 20º
C. 25º
D. 30º
E. 35º

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C
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rajatchopra1994
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Re: If AD = DE and EC = CB as shown above, what is the value of xº? [#permalink] New post   13 Jul 2021, 01:46
Explanation:

In isosceles Triangle ADE, AD = DE and ∠D is 30º
∠DEA = ∠A = z
∠A + ∠DEA + ∠D = 180
z+z+30 = 180
2z = 150
z = 75º

In isosceles Triangle BCE, EC = CB , ∠C is 20º
∠BEC = ∠C = y
∠C + ∠BEC + ∠B = 180
y+y+20 = 180
2y = 160
y = 80º

x+y+z = 180
x = 25º

IMO-C
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If AD = DE and EC = CB as shown above, what is the value of xº? [#permalink] New post   Updated on: 13 Jul 2021, 02:37
In isosceles Triangle ADE, AD = DE angle D is 30
a+a+30 = 180 (Say equal angles are a each)
2a = 150
a = 75

In isosceles Triangle BCE, EC = CB , angle C is 20
b+b+20 = 180 (Say equal angles are b each)
2b = 160
b = 80

x+a+b = 180
x = 25º

IMO (C) is the right answer

Bunuel wrote:

If AD = DE and EC = CB as shown above, what is the value of xº?

A. 15º
B. 20º
C. 25º
D. 30º
E. 35º

Project PS Butler


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Originally posted by sumitkrocks on 13 Jul 2021, 02:16.
Last edited by sumitkrocks on 13 Jul 2021, 02:37, edited 2 times in total.
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rajatchopra1994
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Re: If AD = DE and EC = CB as shown above, what is the value of xº? [#permalink] New post   13 Jul 2021, 02:22
sumitkrocks wrote:
In isosceles Triangle ADE, AD = DE and ∠D is 30º
∠DEA = ∠A = z
∠A + ∠DEA + ∠D = 180
z+z+30 = 180
2z = 150
z = 75º

In isosceles Triangle BCE, EC = CB , ∠C is 20º
∠BEC = ∠C = y
∠C + ∠BEC + ∠B = 180
y+y+20 = 180
2y = 160
y = 80º

x+y+z = 180
x = 25º

IMO (C) is the right answer



Dear sumitkrocks ,

Please do not copy exact answers from above and post it. Always try some different method and post your self made answer.
Bunuel yashikaaggarwal please check.

Regards,
Rajat Chopra
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Re: If AD = DE and EC = CB as shown above, what is the value of xº? [#permalink] New post   13 Jul 2021, 02:45
Thanks for the attention rajatchopra1994 Bunuel
Post edited, hope you are not having any concerns with the post now. My intention was only to save time in typing but agreed its not a right practice.

Good luck.

Cheers


rajatchopra1994 wrote:
sumitkrocks wrote:
In isosceles Triangle ADE, AD = DE and ∠D is 30º
∠DEA = ∠A = z
∠A + ∠DEA + ∠D = 180
z+z+30 = 180
2z = 150
z = 75º

In isosceles Triangle BCE, EC = CB , ∠C is 20º
∠BEC = ∠C = y
∠C + ∠BEC + ∠B = 180
y+y+20 = 180
2y = 160
y = 80º

x+y+z = 180
x = 25º

IMO (C) is the right answer



Dear sumitkrocks ,

Please do not copy exact answers from above and post it. Always try some different method and post your self made answer.
Bunuel yashikaaggarwal please check.

Regards,
Rajat Chopra
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Re: If AD = DE and EC = CB as shown above, what is the value of xº? [#permalink] New post   13 Jul 2021, 02:46
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If AD = DE and EC = CB as shown above, what is the value of xº?

In triangle DAE
angle DAE = angle DEA (isosceles triangle)
30 + 2y = 180
2y = 150
y=75

In triangle CEB
angle CEB = angle CBE (isosceles triangle)
20 + 2z =180
2z = 160
z = 80

Now 75 + 80 + x = 180 (Linear )
x = 25

IMO C
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Re: If AD = DE and EC = CB as shown above, what is the value of xº? [#permalink] New post   13 Jul 2021, 05:49
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To find x, we know DEA + CEB + x = 180
DEA = (180-30)/2 = 75
CEB = (180-20)/2 = 80
Then, x = 180-80-75=25 C
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Re: If AD = DE and EC = CB as shown above, what is the value of xº? [#permalink] New post   13 Jul 2021, 07:35
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Bunuel wrote:

If AD = DE and EC = CB as shown above, what is the value of xº?

A. 15º
B. 20º
C. 25º
D. 30º
E. 35º


IMO C, 0.25min

Simple concepts: Total sum of the angles in a triangle is 180, Line is also 180.
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Re: If AD = DE and EC = CB as shown above, what is the value of xº? [#permalink] New post   14 Jul 2021, 00:04
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Bunuel wrote:

If AD = DE and EC = CB as shown above, what is the value of xº?

A. 15º
B. 20º
C. 25º
D. 30º
E. 35º

Project PS Butler


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In isos triangle DAE, DA = AE
So, 2x + 30 = 180
2x = 150
x = 75
In iso triangle CEB, CE = CB
So, 2x + 20 = 180
2x = 160
x = 80
x + 80 = 30 + 75(Why? Ext. angle = sum of opposite angles in a triangle)
x = 25. IMO, (C)!
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Re: If AD = DE and EC = CB as shown above, what is the value of xº? [#permalink]
14 Jul 2021, 00:04
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