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Quadrilaterals ADEB and ACGF are squares with the same sides. What is the measure of the angle

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Quadrilaterals ADEB and ACGF are squares with the same sides. What is the measure of the angle

by Max@Math Revolution » Mon Jul 13, 2020 1:31 am

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[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
A. 45
B. 55
C. 75
D. 80
E. 90
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Re: Quadrilaterals ADEB and ACGF are squares with the same sides. What is the measure of the angle

by Max@Math Revolution » Tue Jul 14, 2020 11:43 pm
=>

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
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