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Q. (Geometry)
PS- Angles.jpg [ 6.16 KiB | Viewed 3293 times ]
w, x, y, and z are depicted as shown in the above figure. Which one of the following is always true?
A. x + y = \(180^o\)
B. w + z = \(180^o\)
C. x + y < z + w
D. x + y = z + w
E. x + y > z + w
Attachment:
PS- Angles.jpg [ 6.16 KiB | Viewed 3293 times ]
w, x, y, and z are depicted as shown in the above figure. Which one of the following is always true?
A. x + y = \(180^o\)
B. w + z = \(180^o\)
C. x + y < z + w
D. x + y = z + w
E. x + y > z + w
yashikaaggarwal
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Joined: 19 Jan 2020
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Location: India
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02 Sep 2020, 08:28
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In Triangle EAB
Angle E = a
Angle A = 180-y
Angle B = 180-x
Angle E + Angle A + Angle B = 180
a+180-y+180-x = 180
a + 180 = Y + X -----------------------------(1)
In Triangle ECD
Angle E = a
Angle D = 180-W
Angle C = 180-Z
Angle E + Angle D + Angle C = 180
a+180-W+180-Z = 180
a + 180 = W + Z -----------------------------(2)
equating eq 1 and 2
X+Y = W+Z
Answer is D
Angle E = a
Angle A = 180-y
Angle B = 180-x
Angle E + Angle A + Angle B = 180
a+180-y+180-x = 180
a + 180 = Y + X -----------------------------(1)
In Triangle ECD
Angle E = a
Angle D = 180-W
Angle C = 180-Z
Angle E + Angle D + Angle C = 180
a+180-W+180-Z = 180
a + 180 = W + Z -----------------------------(2)
equating eq 1 and 2
X+Y = W+Z
Answer is D
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Diagram.jpeg [ 63.39 KiB | Viewed 3234 times ]
02 Sep 2020, 19:58
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ABCD is a Quadrilateral and sum of the angles of a quadrilateral is always \(360^o\)
\(\angle ADC = 180 - \angle w\) (Sum of angles on a straight line = \(360^o\))
Similarly, \(\angle DCB = 180 - \angle z\) (Sum of angles on a straight line = \(360^o\))
Therefore In quadrilateral ABCD, y + x + (180 - w) + (180 - z) = 360
y + x - w - z + 360 = 360
Therefore, y + x = w + z
Option D
Arun Kumar
\(\angle ADC = 180 - \angle w\) (Sum of angles on a straight line = \(360^o\))
Similarly, \(\angle DCB = 180 - \angle z\) (Sum of angles on a straight line = \(360^o\))
Therefore In quadrilateral ABCD, y + x + (180 - w) + (180 - z) = 360
y + x - w - z + 360 = 360
Therefore, y + x = w + z
Option D
Arun Kumar
