Question

two adjacent angles of a parallelogram are in the ratio 2 is to 3 find the measure of each of the angles in parallelogram pqrs find X ,y ,z and w.
Thanks in advance for those who helped me in this question.​

Answer 1

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PQRS is a parallelogram

We know that, sum of adjacent angles of parallelogram is 180 degree

∴ ∠QPS + ∠PSR = 180°

⇒ x + 110 degree =180°

⇒ x=70°

We know that, opposite angles of a parallelogram are equal.

∴ x = y = 70 degree and z = 110°

⇒ ∠PSR+∠PST=180°

[ Linear pair ]

⇒ 110 degree + w = 180°

⇒ w = 70°

Now,

We get x = 70°, y = 70°, z = 110°, w = 70°

Hope it helps

Answer 2

Correct Question:

• In Parallelogram PQRS, ∠PSR = 110°. Then, Find the measure of each angles of parallelogram PQRS i.e. x , y , z and w.

Given:

• ∠PSR = 110°

To find:

• Measure of angles w , x , y and z?

Solution:

We know that,

Sum of adjacent angles of parallelogram is 180°.

So,

In Parallelogram PQRS,

⇒ ∠QPS + ∠PSR = 180°

⇒ x + 110° = 180°

⇒x = 180° - 110°

⇒ x = 70°

Also,

We know that,

Opposite angles of a parallelogram are equal.

Therefore,

∴ ∠QPS = ∠QRS

⇒ x = y = 70°

Also,

∠PSR = ∠PQR

⇒∠PSR = z = 110°

Now,

⇒ ∠PSR + ∠PST = 180° [ Linear pair ]

⇒ 110° + w = 180°

⇒ w = 180° - 110°

⇒ w = 70°

∴ Hence, measure of angle w , x , y and z is 70° , 70° , 70° and 110° respectively.