In the given figure, AB and CD are
straight lines through the centre o of a
circle. If angleAOC = 80º and angle CDE = 40°,
find (i) angle DCE, (ii) angle ABC.
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Step-by-step explanation:
We show here,
(i) ∠CED=90
0
(Angle in a semicircle is a right angle)
∴∠DCE=90
0
−∠CDE=90
0
−40
0
=50
0
∴∠DCE=∠OCB=50
0
(ii) In ΔBOC,
∠AOC=∠OCB+∠OBC
(Exterior angle of a Δ is equal to the sum of pair of interior opposite angle)
∠OCB=80
0
−50
0
=30
0
[∠AOC=80
0
given]
Hence,∠ABC=30
0
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