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Updated on: 15 Jul 2020, 00:14
Originally posted by MathRevolution on 13 Jul 2020, 02:33.
Last edited by MathRevolution on 15 Jul 2020, 00:14, edited 1 time in total.
Last edited by MathRevolution on 15 Jul 2020, 00:14, edited 1 time in total.
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E
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
49% (01:53) correct
51%
(02:08)
wrong
based on 79
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Not Attempted Yet
[GMAT math practice question]
Quadrilaterals \(□ADEB\) and \(□ACGF\) are squares with the same sides. What is the measure of the angle \(∠x\)?
7.13PS.png [ 10.46 KiB | Viewed 2228 times ]
A. \(45^o\)
B. \(55^o\)
C. \(75^o \)
D. \(80^o\)
E. \(90^o\)
Quadrilaterals \(□ADEB\) and \(□ACGF\) are squares with the same sides. What is the measure of the angle \(∠x\)?
Attachment:
7.13PS.png [ 10.46 KiB | Viewed 2228 times ]
A. \(45^o\)
B. \(55^o\)
C. \(75^o \)
D. \(80^o\)
E. \(90^o\)
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13 Jul 2020, 02:36
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15 Jul 2020, 00:46
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Since \(AB = AC = AD = AF\) and \(∠DAC = ∠BAF\), triangles \(ADC\) and \(ABF\) are congruent. Then we have \(∠ADC = ∠ABF.\)
\(∠x = 180° - ∠DHB = 180° – (360° - ( ∠E + ∠EDH + ∠EBH ))\)
\(= 180° – ( 36° – ( 90° + ∠EDA - ∠ADC + ∠EBA + ∠ABF ) )\)
\(= 180° – ( 360° – ( 90° + 90° - ∠ADC + 90° + ∠ADC ) )\)
\(= 180° – ( 360° – 270° ) = 90°\)
Therefore, E is the correct answer.
Answer: E
Since \(AB = AC = AD = AF\) and \(∠DAC = ∠BAF\), triangles \(ADC\) and \(ABF\) are congruent. Then we have \(∠ADC = ∠ABF.\)
\(∠x = 180° - ∠DHB = 180° – (360° - ( ∠E + ∠EDH + ∠EBH ))\)
\(= 180° – ( 36° – ( 90° + ∠EDA - ∠ADC + ∠EBA + ∠ABF ) )\)
\(= 180° – ( 360° – ( 90° + 90° - ∠ADC + 90° + ∠ADC ) )\)
\(= 180° – ( 360° – 270° ) = 90°\)
Therefore, E is the correct answer.
Answer: E
