In the given figure AB || CD and O is a point joined with B and D, as shown in the figure such that ∠ABO = 35 and ∠CDO = 40°. Reflex ∠BOD = ?

Question

In the given figure AB || CD and O is a point joined with B and D, as shown in the figure such that ∠ ABO = 35 and ∠ CDO = 40°. Reflex ∠ BOD = ?

Philoid · Accepted Answer

Draw a line EF such that EF || AB and EF || CD crossing point O.

ABO + EOB = 180^o(Sum of consecutive interior angles is 180^o)

EOB = 180 – 35 = 145^o

EF || AB such that AO is traversal.

CDO + EOD = 180^o(Sum of consecutive interior angles is 180^o)

EOD = 180 – 40 = 140^o

BOD = EOB + EOD

= 145 + 140

= 285^o