Question

PQRS is a rhombus. If angle PRQ = 50 degree then find tge measure of of angle PSQ

Answer 1

Answer:

Step-by-step explanation pQ = QR in ∆ PQR so angle RPQ = angle PRQ = 50 so angle PQ R = 80 degrees.

As we know that in any parallelogram or in any rhombus opposite angle are equal. So angle PSR = 80. Now diagonal of a rhombus bisects the vertex angles so angle PS Q= QSR = 40 degrees

Answer 2

Given: PQRS is a rhombus. If angle PRQ = 50 degree

To find: The measure of of angle PSQ

Solution:

In a rhombus, the opposite sides are necessarily parallel and equal in length. Also, the opposite angles are equal.

Now, if angle PRQ is 50°, then angle PRS is also 50°. This makes the angles ∠P and ∠R equal to 100. Now, the triangle PQS is isosceles. So, the angles PQS and PSQ are equal. Let them be equal to x. Hence, the angle PSQ can be calculated as follows.

$x+x+100 = 180$

$2x = 80$

$x = 40$

Therefore, the measure of angle PSQ is 40°.