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

1.	In Fig., if AB \|\| CD, CD \|\| EF and y : z = 3 : 7, find x.
Answer» 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°.

Answer»

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°.

Discussion