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Question

In the given figure, BAD=75o, DCF=xo and DEF=yo. Find the values of x and y.
1461515_71fd0b4ac7474dc086cc6b6b7764fd63.png

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Solution

In a cyclic quadrilateral we know that the exterior angle is equal to the interior opposite angle

So we get

BAD=DCF=75o

It can be written as

DCF=x=75o

We get x=75o

We know that the opposite angles of a cyclic quadrilateral is 180o

So we get

DCF+DEF=180o

By substituting the values

75o+DEF=180o

On further calculation

DEF=180o75o

By subtraction

DEF=y=105o

Therefore, the value of x and y is 75o and 105o.

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