The given figure shows a parallelogram PQRS, ST and QU are the bisectors of ∠PSR and ∠PQR respectively.

If SU = 4 cm and QU = 10 cm, then what is the value of (ST + TQ)?
(A) 12 cm               (B) 14 cm                (C) 16 cm             (D) 18 cm
 

Dear Student,

PQRS is a parallelogram. ST and QU are the bisectors of ∠ PSR and ∠ PQR and QU = 10 cm and SU = 4 cm .

∠ PSR = ∠ PQR        (given)

Since, opposite sides of a parallelogram are parallel,

PQSR

⇒TQSU  

Consider ST as transversal, 

∠ QTS + ∠ TSU = 180°          (angles on the same side of a transversal are supplementary) 

Also, ∠ TQU + ∠ SUQ = 180°      (angles on the same side of a transversal are supplementary) 

Since, ∠TSU = ∠TQU 

So, ∠ SUQ = ∠QTS

In quadrilateral TQUS, since a pair of opposite angles are equal and TQSU,

TQUS is a parallelogram.

Hence, TQ = SU and ST = QU

ST + TQ = QU + SU = 10 + 4 = 14 cm.

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