1.

In the adjacent figure, AB is a straight line, O is a point on AB. OC is a ray. Take a point D in the interior of ∠AOC, join OD. Find ∠AOD + ∠DOC + ∠COB.

Answer»

Given ∠AOC and ∠COB are linear pair. 

But ∠AOC = ∠AOD + ∠DOC

FigureTransversalExterior anglesInterior anglesPairs of corresponding anglesPairs of alternative interior anglesPairs of alternative exterior angles
(i)n∠a, ∠e
∠b, ∠f
∠c, ∠g
∠d, ∠h
(ii)∠1, ∠4,
∠5, ∠8

⇒ ∠AOC + ∠COB = 180° (linear pair) 

⇒ ∠AOD + ∠DOC + ZCOB = 180°


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