Question

find the value x, y, z if AB||CD||EF​

Answer 1

lets name the point of the line that touches AB as P , CD as Q and EF as R and S be the other point such that RS touches CD

Given, Angle APQ = 79° = angle CQR( corresponding angles)

and L CQR = L PQD = 79°= z ( vertical angles)

As we can see in the fig L QRF= L QRS + L SRF

therefore 79°= L QRS + 67° (L zrF and L pzD corresponding angles= 79°)

L QRS= 79-67 = 12° =y

Now L EFR = 180°

L QRS +L SRF+ L QRE = 180

67+12+ L QRE= 180°

L QRE =180°-79° = 101°

since L CSR is the corresponding angle opposite to L ERC

L CSR + L ERS =180°

L CSR = 180°- (L ERQ+ L QRS)

L CSR = 180° -(101+12) = 180°- 113 = 67°

L CDE = L DSR + L CSR

180° = L DSR + 67°

L DSR = 180°-67° = 113° = x

This z= 79, y = 12 and x= 113

you can do it easily if you understand the relation between alternate, vertical and corresponding angles , This is just detailed explanation of how it works .