QR = 43
SR = 61
PT = 10
SQ = 10
m/QRS = 25°
m/PQS = 96°
m/RPS = 35°
m/PSQ = 35°
Find QR and SR:
We are given that PO = 24 and PS = 19. Since OP and OS are opposite sides of a parallelogram, we know that QR = PO + PS = 24 + 19 = 43.
Similarly, since PR and PS are opposite sides of a parallelogram, we know that SR = PR + PS = 42 + 19 = 61.
2. Find PT and SQ:
We are given that TQ = 10. Since opposite sides of a parallelogram are equal, PT = SQ = 10.
3. Find the measures of angles QRS, PQS, RPS, and PSQ:
We are given that m/PQR = 106° and m/QSR = 49°. Since the angles of a triangle add up to 180°, we can find the measure of angle PQS:
m/PQS = 180° - m/PQR - m/QSR = 180° - 106° - 49° = 25°
Similarly, we can find the measure of angle RPS:
m/RPS = 180° - m/QSR - m/PRS = 180° - 49° - 35° = 96°
We are given that m/PRS = 35°. Since opposite angles of a parallelogram are equal, we know that m/PSQ = m/PRS = 35°.