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Chapter 5: Q5 (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 are 8,10,118°and 62°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 given figure, PS¯≅QR¯implies that a=8and PQ¯≅SR¯implies that b=10.

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 ∠y≅∠PSRimplies that

y=m∠PSR=62°

05

Step 5. Description of step.

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

m∠PSR+m∠SRQ=18062+x=180x=180−62=118°

Therefore, the values of a, b, x and y are 8,10,118°and62° respectively.

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