Answer :

The value of angle QRU is 102° and the value of angle VUW is 72°.

As we can see, the line QRS and the Line TUv are parallel to each other,

So, the angle ∠wuv and ∠urs are the same side interior angle,

So ∠wuv =∠urs

Also from the properties of the supplementary angles,

∠urs and ∠QRu are supplementary angles,

Thus,

∠urs +∠QRu = 180

4x + 6x = 180

10x = 180

x = 18 degrees

Therefore, the value of angle QRU = 18 * 6 = 102 degrees

and the value of angle VUW = 4 *18 = 72 degrees.

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