Question

In a parallelogram PQRS, if PQ =

3.5 cm, PS =5.3cm, ∠Q = 50o

, find

QR, SR ∠S, ∠P and ∠R.​

Answer 1

Answer:

First,the parallelogram is  a quadrilateral whose opposite sides are parallel

so, QR=PS ; PQ = SR

QR = 5.3cm ; SR = 3.5cm

Then,

the sum of the interior of a parallelogram is 360°

∠Q is equal to ∠S because they are opposite

so ∠S is 50°

∠P is equal to ∠R

360°-50°-50° = 260°

$\frac{260}{2}$ = 130°

∠P = 130°

∠R = 130°

Answer 2

Answer:

Given: A parallelogram PQRS, in which:

1. PQ=3.5 cm
2. PS= 5.3 cm
3. ∠Q = 50°

To find:

1. QR
2. SR
3. ∠S
4. ∠R.​
5. ∠P

Proof:

In ||gram PQRS,

1. PS= QR= 5.3 cm                 [Opposite sides of a ||gram are equal]

Similarly,

    2. PQ= SR = 3.5 cm                [Opposite sides of a ||gram are equal]

Now,

   3. ∠Q = ∠S = 50°                      [Opposite angles of a ||gram are equal]

We have:

= ∠Q + ∠R = 180°                          [ Co-interior angles are supplementary]

                                                     [ Opposite sides of a ||gram are parallel]

⇒ 50° + ∠R = 180°

⇒ ∠R = (180 - 50 )°

    4. ∠R = 130°

Now,

    5. ∠R= ∠P= 130°                       [ Opposite angles of a ||gram are equal]

Hence,

1. QR = 5.3 cm
2. SR = 3.5 cm
3. ∠S = 50°
4. ∠R = ​130°
5. ∠P = 130°

Hope you got that.

Thank You.