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

Step-by-step explanation:

y : z = 3 : 7

[Given]

Let the common multiple be m ∴ ∠j = 3m and ∠z = 7m ….

(i) line AB || line EF and line PQ is their transversal

[Given]

∠x = ∠z ∴ ∠x = 7m …..

(ii) [From (i)] line AB || line CD and line PQ is their transversal

[Given]

∠x + ∠y = 180°

∴ 7m + 3m = 180° ∴ 10m = 180° ∴ m = 18°

∴ ∠x = 7m = 7(18°) [From (ii)]

∴ ∠x = 126°

Answer 2

Answer:y :

z = 3 : 7 [Given]  

Let the common multiple be m  

∴ ∠j = 3m and ∠z = 7m ….(i)

line AB || line EF and line PQ is their transversal [Given]

∠x = ∠z  ∴ ∠x = 7m …..(ii)

[From (i)]  line AB || line CD and line PQ is their transversal [Given]  

∠x + ∠y = 180°  ∴ 7m + 3m = 180°

∴ 10m = 180°  ∴ m = 18°  ∴ ∠x = 7m = 7(18°) [From (ii)]  

∴ ∠x = 126