In the given figure, AB || CD. If ∠ AOC = 30° and ∠ OAB = 100°, then ∠ OCD = ?

Question

Philoid · Accepted Answer

From O, draw E such that OE || CD || AB.

OE || CD and OC is traversal.

So,

DCO + COE = 180 (co –interior angles)

x + COE = 180

COE = (180 – x)

Now, OE || AB and AO is the traversal.

BAO + AOE = 180 (co –interior angles)

BAO + AOC + COE = 180

100 + 30 + (180 – x) = 180

180 – x = 50

X = 180 – 50 = 130^O