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- Step-by-step explanation:
- In ∆TQR angle TQR = 40° ( given )
- and angle QTR = 90 ° ( given )
- we know that the sum of angles of a triangle is 180° .
- angle QTR + angle QRT + angle TQR = 180 °
- 40° + 90° + angle QRT = 180 °
- 130 ° + angle QRT = 180°
- angle QRT = 50 ° so , angle x = 50 °
- In triangle PSR
- angle SPR + angle PRS = angle PSQ
- angle PSQ = 80 °
- so angle Y = 80 °
- and QSR is a straight line
- so angle z = 180 - 80 = 100°
- hope this will help you
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Answer: let ot and ps intersec t at o
angle ptq = 90 degree linear pair
then angle pot =(180-90+30)=60 {angle sum property}
angle soq=angle pot=60 degree (vertically opposite)
y=(180-40+60)=80
z=(180-80)=100 degree (linear pair)
now in quadrilateral otsr we have all angles sum to 360 degree
angle o +angle s + angle r + angle t=360
60 degree + 100 degree + x degree + 90 degree=360 degree
x degree=(360 -90 -100 -60 )degree
x= 360-250=110 degree
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