Question

∆PQRS is a parallelogram. PQ = 3.5, RS = 5.3, ∠Q = 50° then find the lengths of remaining

sides and measures of remaining angles.​

Answer 1

Given:

Parallelogram PQRS

Length of PQ = 3.5 units

Length of PS = 5.3 units

Measure of ∠Q = 50°

To find:

The lengths of remaining sides and measures of other angles.

Solution:

In a parallelogram, there are two pairs of parallel sides and the opposite sides are equal. The opposite angles are equal and also interior angles on the side of the transversal are supplementary.

Here, we have a parallelogram PQRS whose sides PQ and PS are given. The side opposite to PQ is SR and hence the length of SR will be equal to the length of PQ.

$PQ =3.5$    (given)

∴ $SR=3.5$  (opposite sides are equal and parallel)

The length of PS is given as 5.3 units and the side opposite to PS is QR. Its length will also be equal because it is on the opposite side of PS and is parallel to it.

$PS=5.3$   (given)

∴ $QR=5.3$   (opposite sides are equal and parallel)

The measure of ∠Q is given as 50°. The angle opposite to Q is ∠S. Hence, ∠S = 50° because, in a parallelogram, opposite angles are equal.

Now, $<Q + <R = 180$ (interior angles on the same side of the transversal are supplementary)

$50+<R=180$

$<R=180-50$

$<R=130$

Now, the angle opposite to R is ∠P. Since ∠R = 130°, ∠P = 130° because opposite angles in a parallelogram are equal.

Hence, $QR=5.3$ , $SR=3.5$, ∠S = 50°, ∠R = 130°, and, ∠P = 130°.

The lengths of remaining  sides and measures of remaining angles in parallelogram PQRS are ​QR = 5.3, SR = 3.5, ∠S = 50°, ∠R = 130°, and,

∠P = 130°.

Answer 2

Answer:

PQRS is parallelogram seg. SR = 5.8 cm then find the length of seg. PQ