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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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  35% (medium)

Question Stats:

67% (01:35) correct 33% (02:02) wrong based on 35 sessions

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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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Capture1.JPG [ 31.18 KiB | Viewed 650 times ]

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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.
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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:
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(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 518 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= &nbs [#permalink] 15 Mar 2018, 19:19
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If O is the center and AB parallel to CD, then x=

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