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# Segment BD and AE intersect at C, as shown, AB = BC = CD = CE, and ∠A

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Joined: 02 Sep 2009
Posts: 58428
Segment BD and AE intersect at C, as shown, AB = BC = CD = CE, and ∠A  [#permalink]

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28 Mar 2019, 23:43
00:00

Difficulty:

35% (medium)

Question Stats:

63% (02:17) correct 38% (02:40) wrong based on 15 sessions

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Segment BD and AE intersect at C, as shown, AB = BC = CD = CE, and ∠A = 5/2*∠B. What is the degree measure of ∠D?

(A) 52.5
(B) 55
(C) 57.7
(D) 60
(E) 62.5

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2648b032deb3bc4fba6f53bcb3b07b32bcfad484.png [ 6.23 KiB | Viewed 302 times ]

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Re: Segment BD and AE intersect at C, as shown, AB = BC = CD = CE, and ∠A  [#permalink]

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29 Mar 2019, 03:11
1
∆ABC
angle A= 5/2 * angle b
angle b = 2* angle a/5
angle a = x and angle a= angle c so

2x+2x/5 = 180
x= 75 and angle B = 30
∆CED
angle C = 75 and
75+2x=180
angle D ; 52.5 IMO A

Bunuel wrote:

Segment BD and AE intersect at C, as shown, AB = BC = CD = CE, and ∠A = 5/2*∠B. What is the degree measure of ∠D?

(A) 52.5
(B) 55
(C) 57.7
(D) 60
(E) 62.5

Attachment:
Re: Segment BD and AE intersect at C, as shown, AB = BC = CD = CE, and ∠A   [#permalink] 29 Mar 2019, 03:11
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