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Question

In the given figure, AB and CD are straight lines through the
centre O of a circle. If AOC=80o and CDE=40o, find ABC
1715461_0a7aa3e6fb304d84bef229d4416c4325.png

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Solution

We know that AOC and BOC from a linear pair

It can be written as

BOC=180o80o

By subtraction

BOC=100o

Using the angle sum property

ABC+BOC+DCE=180o

By substituting the values

ABC+100o+50o+=180o

On further calculation

ABC=180o100o50o

By subtraction

ABC=180o150o

So we get

ABC=30o


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