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13 Jul 2021, 01:30
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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)!
Difficulty:
5%
(low)
Question Stats:
88% (00:52) correct
12%
(01:51)
wrong
based on 76
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Not Attempted Yet
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
Attachment:
1.png [ 6.97 KiB | Viewed 2230 times ]
13 Jul 2021, 01:46
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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
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
Updated on: 13 Jul 2021, 02:37
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.
Last edited by sumitkrocks on 13 Jul 2021, 02:37, edited 2 times in total.
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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
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
