Question

In the given figure AB | CD. Transversal PO intersects AB at E and CD at F. Given, ZCFQ = 47°, the measure of x and y respectively are (2) 30°, 150 (b) 37°, 143 (c) 47°, 133 (d) 399, 141° ​

Answer 1

Answer:

AB∣∣CD and PQ is transversal

∠DMQ=100

o

[ Given]

∠DMQ=∠CML=100

o

[ Vertically opposite angles]

∠CML=∠ALP=100

o

[ Corresponding angles]

∠ALP=∠MLB=100

o

[ Vertically opposite angles]

∠CMQ=180−100=80

o

[sum of angle on a straight line is 180^o$$]

∠CMQ=∠LMD=80

o

[ Vertically opposite angles]

∠LMD=∠PLB=80

o

[ Corresponding angles]

∠PLB=∠ALM=80

o

[ Vertically opposite angles]

∴ ∠DMQ=∠CML=∠ALP=∠MLB=100

o

and ∠CMQ=∠LMD=∠ALM=∠PLB=