the quadrilateral parallelogram has measurements and angles, PQ=24, PS=19, TQ=10,

Question

angle PQR=106 degrees, angle QSR=49 degrees, and angle PRS=35 degrees. What are the measurements of QR,SR,PT,SQ and angles QRS,PQS,RPS,PSQ?

Answer 1

To find the missing measurements and angles, we can use the properties of parallelograms. In a parallelogram, opposite sides are equal in length and opposite angles are equal in measure.

1. QR = PQ = 24 units
2. SR = PS = 19 units
3. PT = SQ = 10 units

Now, let's find the missing angles:

1. angle QRS = angle PQR = 106 degrees
2. angle PQS = angle RPS = 74 degrees (180 degrees - angle PQR)
3. angle RPS = angle PRS = 35 degrees

Therefore, the measurements of QR = 24 units, SR = 19 units, PT = 10 units, SQ = 10 units

And the angles QRS = 106 degrees, PQS = 74 degrees, RPS = 35 degrees, PSQ = 74 degrees.