Answer:
Step-by-step explanation:
PQRS is a parallelogram with QR = 6 cm, QT = 3 cm and ∠PSR = 115°.
a). By the property of a parallelogram,
"Diagonals of a parallelogram bisect each other"
QT = TS
QS = 2(QT)
= 2(3)
= 6 cm
b). "Adjacent angles of a parallelogram are supplementary"
m∠PSR + m∠SRQ = 180°
115° + m∠SRQ = 180°
m∠SRQ = 65°
c). Since, SQ = SR = 6 cm
m∠QSR = m∠SRQ [Opposite angles of the equal sides of an isosceles triangle]
m∠QSR = 65°
By applying triangle sum theorem in ΔQSR,
m∠SQR + m∠QRS + m∠QSR = 180°
m∠SQR + 65° + 65° = 180°
m∠SQR = 50°
