Question

In the given figure, PQRS is a rectangle.
QS = QT, angle QTS = 50°. Find angle RST and
angle RQT​

Answer 1

Given :   PQRS is a rectangle.

QS = QT, angle QTS = 50°

Reflex  PST = 260°

To Find : angle RST and  angle RQT​

Solution:

Reflex  PST = 260°

=> ∠PST =360°  -  260°  =  100°  

∠PST  =  ∠PSR +  ∠RST

∠PSR = 90°  as PQRS is a rectangle

=> 100°   = 90°   + ∠RST

=>  ∠RST = 10°

QS = QT

=> ∠QST = ∠QTS

=> ∠QST = 50°

∠QST  = ∠QSR +  ∠RST

=> 50°   = ∠QSR   + 10°

=> ∠QSR = 40°

=>  ∠SQR  = 50°   ( as sum of angles in ΔSRQ = 180° and ∠SRQ = 90°)

∠QST = ∠QTS = 50°

∠QST +  ∠QTS  + ∠SQT = 180°  Sum of angles of triangles

=> ∠SQT = 80°

∠SQT = ∠SQR + ∠RQT

=>  80° = 50° + ∠RQT

=> ∠RQT = 30°

∠RST = 10°  and ∠RQT = 30°

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