Find the value of x in the diagram below.

1.	Find the value of x in the diagram below.
Answer» ∠PQS = ∠EPT = 130° [Corresponding angle] ∠PQS + ∠SQR = 180° [Linear pair] SQR = 180 – 130 ∠SQR = 50° ∠QRS + ∠FRS = 180° [Linear pair] ∠QRS + 90° =180° ∠QRS = 180 – 90 ∠QRS = 90° ∠SQR+ ∠QRS +∠QSR = 180° [Sum of the angles of triangle is 180° ] 50 + 90 + ∠QSR = 180° 140 + ∠QSR = 180° ∠QSR = 180 – 140 ∠QSR =40° ∠TSD = ∠QSR [Vertically opposite angles] x = 40°.

Answer»

∠PQS = ∠EPT = 130° [Corresponding angle]

∠PQS + ∠SQR = 180° [Linear pair]

SQR = 180 – 130

∠SQR = 50°

∠QRS + ∠FRS = 180°

[Linear pair] ∠QRS + 90° =180°

∠QRS = 180 – 90

∠QRS = 90°

∠SQR+ ∠QRS +∠QSR = 180°

[Sum of the angles of triangle is 180° ]

50 + 90 + ∠QSR = 180°

140 + ∠QSR = 180°

∠QSR = 180 – 140

∠QSR =40°

∠TSD = ∠QSR [Vertically opposite angles]

x = 40°.

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