3. In the given figure, AB || CD and a transversal PQ cuts AB at E and CD at F. If ZPEB = 70°, ZBEG = 30°, ZEFG = 25°, ZGFD = rº and ZEGF = yº, find the values of x and y.
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Answer:
Step-by-step explanation:
As per diagram 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
[ Vertically opposite angles]
∴ ∠DMQ=∠CML=∠ALP=∠MLB=100
o
and ∠CMQ=∠LMD=∠ALM=∠PLB=80
o
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