Math, asked by devika08mathur, 8 hours ago

find the value of x, y and z​

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Answers

Answered by rahulchandragiri6
1

Given :-

A quadrilateral ABCD in which AB//CD and AD//BC and the angles of the quadrilateral is x, y, z, w. DC is extended to a certain point in which the angle between quadrilateral and the extended line is 53 degrees.

To find :-

The values of the angles x, y, z in the given quadrilateral.

Process to find :-

Here, the given quadrilateral is a parallelogram. All are parallel sides to each other.

Let the extended point will be E.

Then, Angle BCE + Angle BCD = 180 degrees. (Linear pair)

53 + w = 180

w = 180 - 53

w = 127

In a parallelogram,

Opposite angles are equal.

Therefore, x = w and y = z

x = 127

According to the quadrilateral angle sum rule,

x + y + z + w = 360

127 + 127 + z + w = 360

254 + 2y = 360

Because of y = z

2y = 360 - 254

2y = 106

y = 53

Therefore, y = z,

z = 53

Conclusion:-

The answers are

x = 127

y = 53

z = 53

HOPE IT HELPS

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