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28 Jul 2020, 01:48
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[GMAT math practice question]
The figure shows the points \(A, B, C, … , G\) and \(∠B = 70°, ∠C = 68°, ∠D = 78°, ∠E = 82°, ∠F = 86°\) and \(∠G = 88°\). What is \(∠A\)?
7.28PS.png [ 11.26 KiB | Viewed 3101 times ]
A. \(58°\)
B. \(60° \)
C. \(68°\)
D. \(70°\)
E. \(88°\)
The figure shows the points \(A, B, C, … , G\) and \(∠B = 70°, ∠C = 68°, ∠D = 78°, ∠E = 82°, ∠F = 86°\) and \(∠G = 88°\). What is \(∠A\)?
Attachment:
7.28PS.png [ 11.26 KiB | Viewed 3101 times ]
A. \(58°\)
B. \(60° \)
C. \(68°\)
D. \(70°\)
E. \(88°\)
yashikaaggarwal
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28 Jul 2020, 02:47
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In order to find Angle A
We need to find value of the angles of quadrilateral AFDJ
Where angle D = 78 and F = 86
In quadrilateral BGEK
B = 70, E = 82, G = 88 ,
K = Sum total of all sides - B - E - G
K = 360 - 70 - 82 - 88
K = 120 -------------(1)
In triangle CKJ
Exterior angle at K = Angle C + Angle J
Angle J = Exterior angle K - Angle C
Angle J = 120 - 68
Angle J = 52
Exterior angle J = 180-52 = 128 ----------(2)
Putting value of J in quadrilateral AFDJ
Angle A = Sum total of all sides - F - D - J
Angle A = 360 - 78 - 86 - 128
Angle A = 68.
Posted from my mobile device
We need to find value of the angles of quadrilateral AFDJ
Where angle D = 78 and F = 86
In quadrilateral BGEK
B = 70, E = 82, G = 88 ,
K = Sum total of all sides - B - E - G
K = 360 - 70 - 82 - 88
K = 120 -------------(1)
In triangle CKJ
Exterior angle at K = Angle C + Angle J
Angle J = Exterior angle K - Angle C
Angle J = 120 - 68
Angle J = 52
Exterior angle J = 180-52 = 128 ----------(2)
Putting value of J in quadrilateral AFDJ
Angle A = Sum total of all sides - F - D - J
Angle A = 360 - 78 - 86 - 128
Angle A = 68.
Posted from my mobile device
Attachments
IMG_20200728_151255.jpg [ 1.9 MiB | Viewed 3012 times ]
29 Jul 2020, 08:41
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Consider the triangle in which we have angle A. Let the other 2 angles of that triangle be x and y.
x+y +A = 180
Now :
If you observe closely, the quadrilaterals formed angles : B D F & something else (Lets call it L)
So B+D+F+L = 360
L = 360-234 = 126
Similarly for the other "unseen" quadrilateral : ACE "M"
M = 360- 238 = 122
Now: A +x = 122 and A +y = 126
So 2A +x+y = 248
But A +x+y = 180
So A = 248-180 = 68
Hope this helps!
x+y +A = 180
Now :
If you observe closely, the quadrilaterals formed angles : B D F & something else (Lets call it L)
So B+D+F+L = 360
L = 360-234 = 126
Similarly for the other "unseen" quadrilateral : ACE "M"
M = 360- 238 = 122
Now: A +x = 122 and A +y = 126
So 2A +x+y = 248
But A +x+y = 180
So A = 248-180 = 68
Hope this helps!
