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11 Jun 2020, 01:40
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C
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[GMAT math practice question]
Quadrilateral \(ABCD\) is a parallelogram. Point \(E\) is on line \(BC\), line \(DE\) bisects \(∠D\), and \(AF\) is perpendicular to \(DE.\) If \(∠C = 115^o\), what is the measure of the angle \(∠BAF\)?
6.11PS.png [ 8.35 KiB | Viewed 1781 times ]
A. \(32.5^o \)
B. \(45.5^o\)
C. \(57.5^o\)
D. \(58^o \)
E. \(59.5^o\)
Quadrilateral \(ABCD\) is a parallelogram. Point \(E\) is on line \(BC\), line \(DE\) bisects \(∠D\), and \(AF\) is perpendicular to \(DE.\) If \(∠C = 115^o\), what is the measure of the angle \(∠BAF\)?
Attachment:
6.11PS.png [ 8.35 KiB | Viewed 1781 times ]
A. \(32.5^o \)
B. \(45.5^o\)
C. \(57.5^o\)
D. \(58^o \)
E. \(59.5^o\)
yashikaaggarwal
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11 Jun 2020, 01:53
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Opposite angles if parallelogram are equal.
Therefore Angle C = Angle A = 115° ----------------(1)
Angle B = Angle D
Angle A+B+C+D = 360
115+115+B+D = 360
2B = 130
B = 65° = D ------------(2)
DE bisects Angle D
Therefore,
Angle CDE = Angle ADE
Angle CDE + Angle ADE = 65
2*Angle CDE = 65
Angle CDE = 32.5 = Angle ADE --------(3)
In triangle AFD
Angle AFD = 90° (perpendicular)
Angle ADF = 32.5° {ADE=ADF}
Angle DAF = 180-90-32.5 (angle sum property)
Angle DAF = 57.5
Angle A = Angle DAF + Angle BAF
115 = 57.5+Angle BAF
Angle BAF = 57.5
Answer is C
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Therefore Angle C = Angle A = 115° ----------------(1)
Angle B = Angle D
Angle A+B+C+D = 360
115+115+B+D = 360
2B = 130
B = 65° = D ------------(2)
DE bisects Angle D
Therefore,
Angle CDE = Angle ADE
Angle CDE + Angle ADE = 65
2*Angle CDE = 65
Angle CDE = 32.5 = Angle ADE --------(3)
In triangle AFD
Angle AFD = 90° (perpendicular)
Angle ADF = 32.5° {ADE=ADF}
Angle DAF = 180-90-32.5 (angle sum property)
Angle DAF = 57.5
Angle A = Angle DAF + Angle BAF
115 = 57.5+Angle BAF
Angle BAF = 57.5
Answer is C
Posted from my mobile device
11 Jun 2020, 11:39
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Angle bisectors of consecutive angles of parallelogram makes 90* with each other.
Hence, BAF = 115/2 = 57.5*
Hence, BAF = 115/2 = 57.5*
MathRevolution
