find the value x, y, z if AB||CD||EF
Answers
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 .