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in Lines and Angles by (65.5k points)

In Fig., if AB || CD, CD || EF and y : z = 3 : 7, find x.

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PQ straight line, intersects AB||CD]|EF at points R, S, T. 

If y : z = 3 : 7, then value of ‘x’ = ? 

PQ straight line intersects CD||EF at S and T. 

∴ ∠CSR = ∠DST = y (∵ vertically opposite angle) 

But, ∠DST + ∠STF = 180° 

(∵ Sum of interior angles in the same side) 

∴ y + z = 180° 

But, y : z = 3 : 7. 

Sum of ratio 3 + 7 = 10 

If ratio 10 means 180 

If ratio 9 means ?

\(\frac{180\times3}{10}\) = 54°

∴ y = 54° y + z = 180 

54 + z = 180 

∴ z = 180 – 54 

∴ z = 126° 

But, x + y = 180 

(∵ Sum of interior angles on one side) 

x + 54 = 180 

∵ x = 180 – 54 

∵ x = 126°.

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