Question

In the given figure, TU II SR and TR II SV,then the value of a and b isIn the given figure, TU II SR and TR II SV,then the value of a and b is

Answer 1

Answer:

a = 115° and b = 40°

Step-by-step explanation:

As TU║SR and TR is the transversal,

∠UTR and ∠TRS are co-interior angles

∴ ∠UTR + ∠TRS = 180

∴ 90° + ∠TRS = 180

∴ ∠TRS = 180 - 90°

∴ ∠TRS = 90°

As TQ and PS are intersecting lines,

∠TRS and ∠PRQ are vertically opposite angles

∴ ∠TRS = ∠PRQ

∴ ∠PRQ = 90°

In ΔPQR,

∠QRP + ∠RPQ + ∠PQR = 180°

∴ 90° + 50° + b = 180°

∴ b = 180° - 140°

∴ b = 40°

By construction we can extend TU so that it intersects at X

As TR║SV and RS is tranversal

∠TRS and ∠VSR are co-interior angles

∴ ∠TRS + ∠VSR = 180°

∴ 90° + ∠VSR = 180°

∴ ∠VSR = 90°

As TU║SR, TX║SR. Hence,

∠VXT and ∠VSR are corresponding angles

∴ ∠VXT = ∠VSR

∴ ∠VXT = 90° = ∠VXU

In ΔVXU

∠VUT = ∠UVX + ∠VXU (exterior angle property)

∴ a = 25° + 90°

∴ a = 115°

Hope it helped!!!

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