AB || CD || EF and GH || KM If HGB =75 and KHD = 40 Show that HKM - Maths - Lines and Angles

Question

AB || CD || EF and GH || KM If HGB =75 and KHD = 40 Show that
HKM = 145

Manbar Singh · Accepted Answer

We have,AB ∥ CD ∥ EF  and  GH ∥ KM
Produce GH to L and KM to N
Since CD ∥ AB and HG is a transversal
∴ ∠ HGB + ∠ GHD = 180°  Sum of consecutive interior angles on sameside of transversal is 180°⇒ 75° + ∠ GHD = 180°⇒ ∠ GHD = 105°Since GL ∥ MN  and  HK is a transversal,So, ∠ HKM = ∠ GHK   Alternate Interior Angles⇒ ∠ HKM = ∠ GHD + ∠ KHD⇒ ∠ HKM = 105° + 40°⇒ ∠ HKM = 145°

AB || CD || EF and GH || KM. If HGB =75 and KHD = 40 Show that HKM = 145