Question

Line AB || line CD || line EF and line QP is their transversal. If y : z = 3 : 7 then find the measure of ∠x. 

Answer 1

line AB || line EF      ...(Given)

And the line QP is their transversal.

∴ ∠x ≅ ∠z     ...(Alternate angles)  

∠y : ∠z = 3 : 7    ...(Given)

∴ ∠y = ∠x = 3 : 7   

Let m be a common multiple of the ratio 3 : 7.

∴ ∠y = 3m, ∠x = 7m

line AB || line CD     ...(Given)

And the line QP is their transversal.

∴ ∠x + ∠y = 180°    ...(interior angle theorem)

∴ 7m + 3m = 180° 

∴ 10m = 180°

∴ m = `(180°)/10`

∴ m = 18°

∠x = 7m

∴ ∠x = 7 × 18°

∴ ∠x = 126°