7
Question
In the given figure, XY || ST and UV || XZ, ∠UVT = 75° and ∠TSZ = 50°. Compute ∠XZY + ∠SXY.
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Solution
The correct option is C 125°
Given, XY||ST,
By taking XZ as transversal, We can say
∠TSZ=∠SXY --- (Corresponding angles)
⟹ ∠SXY = 50° --- (∵ ∠TSZ = 50° )
Now,
UV||XZ
By taking YZ as transversal, We can say
∠UVT=∠XZY --- (Corresponding angles)
⟹∠XZY = 75° --- (∵ ∠UVT = 75° )
Now, We have to find ∠XZY + ∠SXY
⟹∠XZY + ∠SXY = 50° + 75° = 125°
Given, XY||ST,
By taking XZ as transversal, We can say
∠TSZ=∠SXY --- (Corresponding angles)
⟹ ∠SXY = 50° --- (∵ ∠TSZ = 50° )
Now,
UV||XZ
By taking YZ as transversal, We can say
∠UVT=∠XZY --- (Corresponding angles)
⟹∠XZY = 75° --- (∵ ∠UVT = 75° )
Now, We have to find ∠XZY + ∠SXY
⟹∠XZY + ∠SXY = 50° + 75° = 125°
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