Question

find the value of x, y and z​

Answer 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