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Chapter 5: Q6 (page 169)

PQRS is a parallelogram. Find the values of a, b, x and y.

Short Answer

Expert verified

The values of a, b, x and y are8,15,80° and 70°respectively.

Step by step solution

01

Step 1. Apply property of parallelogram.

The opposite sides of a parallelogram are congruent.

02

Step 2. Description of step.

In the given figure, PS¯≅QR¯implies that a=8and PQ¯≅SR¯implies thatb=15.

03

Step 3. Apply property of parallelogram.

The opposite angles of a parallelogram are congruent.

04

Step 4. Description of step.

From the given figure, it can be observed that ∠x≅∠QPSimplies that

x=m∠QPS=80°

05

Step 5. Description of step.

Both pairs of opposite sides of a parallelogram are parallel, that is, PS¯||QR¯and SQ¯is a transversal then same side interior angles are supplementary.

m∠PQR+m∠QRS=18030+y+80=180y=180−110=70°

Therefore, the values of a, b, x and y are 8,15,80°and 70°respectively.

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