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If O is the center and AB parallel to CD, then x=

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If O is the center and AB parallel to CD, then x=  [#permalink]

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New post Updated on: 15 Mar 2018, 20:57
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Question Stats:

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If O is the center and AB parallel to CD, then x=
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(A) 40
(B) 50
(C) 60
(D) 70
(E) 80

Attachment:
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Originally posted by itisSheldon on 15 Mar 2018, 08:13.
Last edited by Bunuel on 15 Mar 2018, 20:57, edited 1 time in total.
Edited the question.
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Re: If O is the center and AB parallel to CD, then x=  [#permalink]

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New post 15 Mar 2018, 08:26
itisSheldon wrote:
If O is the center and AB parallel to CD, then x=
Attachment:
The attachment Capture1.JPG is no longer available

(A) 40
(B) 50
(C) 60
(D) 70
(E) 80



Now central angle DOB and angle at circumference BAD have SAME chord BD, so angle BAD = 20/2 = 10

AB ll CD so angle BAD = angle CDA =10

In triangle CED , DE is DIAMETER, so angle DCE = 90

take triangle CDx ... SUM = 180 = C+D+x=90+10+x......x=80

E
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Re: If O is the center and AB parallel to CD, then x=  [#permalink]

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New post 15 Mar 2018, 19:19
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itisSheldon wrote:
If O is the center and AB parallel to CD, then x=

(A) 40
(B) 50
(C) 60
(D) 70
(E) 80

Attachment:
circlewithx.JPG
circlewithx.JPG [ 42.03 KiB | Viewed 1088 times ]

Another way:

• ∠ AOD = 160° (180° = straight line. ∠ BOD = 20°. (180° - 20°) = 160°

• ∆AOD has two congruent angles (opposite equal sides) that = 10°
-- ∠AOD of ∆AOD = 160°
-- Interior angle degrees remaining: (180° - 160°) = 20°, which must be split between two congruent angles
-- The triangle has two equal sides, both radii. Side AO = OD
-- Angles opposite equal sides are equal
-- ∠BAD = 10° = ∠ADE

• The hypotenuse of inscribed ∆CDE is the circle's diameter. Hence it is a right triangle.
-- ∠ C = 90°

• ∠BAD = ∠CDA - they are alternate interior angles of parallel lines cut by a transversal
-- AB || CD
-- the transversal is line segment AD
-- ∠BAD = 10° = ∠CDA = 10°

x = 80. It is the third angle of ∆CDF
The two known angles, in degrees, measure 90 and 10
90° + 10° = 100°
(180° - 100°) = 80°

Answer D
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Re: If O is the center and AB parallel to CD, then x=   [#permalink] 15 Mar 2018, 19:19
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