Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB =55°, then ∠BOD =

Question

Line segments AB and CD intersect at O such that AC || DB . If &#x2220; CAB = 45&#xB0; and &#x2220; CDB =55&#xB0;, then &#x2220; BOD =

Philoid · Accepted Answer

AC ‖ BD

∠CAD = 45^o

∠CDB = 55^o

∠2 = ∠CAD (Alternate angle)

∠2 = 45^o

In

∠BOD + ∠2 + ∠CDB = 180^o

∠BOD + 45^o + 55^o = 180^o

∠BOD + 100^o = 180^o

∠BOD = 180^o – 100^o

= 80^o

Line segments AB and CD intersect at O such that AC || DB. If ∠CAB = 45° and ∠CDB =55°, then ∠BOD =