Question

5) PQRS is a rectangle. Diagonal PR measures (2x+2)cm and
diagonal QS measures (4x - 8)cm Find the measures of PR
and QS.​

Answer 1

Answer:

To find ∠PQO and ∠PSQ.

PQRS is a rectangle, and O is the intersection point of diagonals PR and SQ.

PR=SQ [Diagonals of rectangle are equal]

PO=Qo [Diagonals of rectangle bisect each other]

∴∠PQO=∠OPQ→(1) [Angles opposite to equal sides]

In △POQ ,

∠PQO+∠POQ+∠OPQ=180

∘

2∠PQO+110

∘

=180

∘

[From (1)]

∠PQO=

2

180

∘

−110

∘

=35

∘

Now, in △PQS

∠PQS+∠QPS+∠PSQ=180

∘

35

∘

+90

∘

+∠PSQ=180

∘

∠PSQ=180

∘

−125

∘

55

Answer 2

Step-by-step explanation:

To find ∠PQO and ∠PSQ.

PQRS is a rectangle, and O is the intersection point of diagonals PR and SQ.

PR=SQ [Diagonals of rectangle are equal]

PO=Qo [Diagonals of rectangle bisect each other]

∴∠PQO=∠OPQ→(1) [Angles opposite to equal sides]

In △POQ ,

∠PQO+∠POQ+∠OPQ=180

∘

2∠PQO+110

∘

=180

∘

[From (1)]

∠PQO=

2

180

∘

−110

∘

=35

∘

Now, in △PQS

∠PQS+∠QPS+∠PSQ=180

∘

35

∘

+90

∘

+∠PSQ=180

∘

∠PSQ=180

∘

−125

∘

=