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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掳 and 70掳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炉鈮�QR炉implies that a=8and PQ炉鈮�SR炉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 鈭�x鈮�鈭�QPSimplies that

x=m鈭�QPS=80掳

05

Step 5. Description of step.

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

m鈭�PQR+m鈭�QRS=18030+y+80=180y=180鈭�110=70掳

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

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