Q.12. In the given figures, $AB\parallel CD$, find the value of unknown.
(a)

(b)

(c)

a and b draw a line FE to E parallel to AB and CD so AB || FE| CD

a) < FEA = < BEA = 45 ( since FE  || AB ) and < FEC = <ECD = 50 degrees ( since FE || AB ) alternate interior angles are equal

so < AEC = < FEA + < CEA = 45 + 90 = 135 degrees
x + <AEC = 360 degrees
x  = 360 - 135 = 225

b) <FEB = <AEB = 30  since FE || AB
<FED = <EDC = 70 since FE || DC
x = < FEB + < FED = 30 + 70 = 100 degrees

c) Since AB|| CD
and Assuming AOD and COB to be straight lines
x=30 and z=60 since x and <ADC are alternate interior angles and z and <ABC are also alternate interior angles and AB || CD
triangle angles are x, y and 60
x = 30
so y = 180 - (60+30) = 90
x= 30, y = 90 , z = 60
<A =