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# In the diagram below, AB and CD are parallel to each other. What is

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In the diagram below, AB and CD are parallel to each other. What is  [#permalink]

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24 Jul 2017, 23:14
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25% (medium)

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90% (02:05) correct 10% (01:32) wrong based on 40 sessions

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In the diagram below, AB and CD are parallel to each other. What is the measure of ∠KXY?

(1) ∠LXB and ∠AXK are equal and ∠LXB is 6◦ greater than ∠YXL.
(2) XY is perpendicular to AB.

Attachment:

2017-07-25_1013.png [ 10.21 KiB | Viewed 3840 times ]

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Re: In the diagram below, AB and CD are parallel to each other. What is  [#permalink]

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25 Jul 2017, 05:27
Bunuel wrote:
In the diagram below, AB and CD are parallel to each other. What is the measure of ∠KXY?

(1) ∠LXB and ∠AXK are equal and ∠LXB is 6◦ greater than ∠YXL.
(2) XY is perpendicular to AB.

Attachment:
2017-07-25_1013.png

(1) We can't know the value of ∠KXY. Insufficient.

For example, if ∠LXB = ∠AXK = 60◦, we have ∠YXL = 54◦ so ∠KXY = 6◦
If ∠LXB = ∠AXK = 30◦, we have ∠YXL = 24◦ so ∠KXY = 96◦

(2) WE can't know the value of ∠KXY. Insufficient.

Combine (1) and (2)

Since ∠YXL = ∠LXB - 6◦ and ∠YXL + ∠LXB = 90◦ we have ∠LXB = 48◦ so ∠AXK = 48◦.

Hence ∠KXY = 90◦ - ∠AXK = 46◦. Sufficient.

The answer is C.
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Re: In the diagram below, AB and CD are parallel to each other. What is   [#permalink] 25 Jul 2017, 05:27
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# In the diagram below, AB and CD are parallel to each other. What is

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