ABCD is a cylic quadrilateral in which BC is parallel to AD, angle ADC = $110^{o}$ and angle BAC = $50^{o}$ . Find angle DAC and angle DCA.

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Solution

We have ABCD a cyclic quadrilateral and BC II AD
The sum of opposite angles of cyclic quadrilateral is 180 degree
This gives angle ABC=180-110=70 degree
The triangle ABC has angle ABC=70 and angle BAC=50
Hence angle BCA=180 - 70 - 50 = 60 degree
We know BC II AD and angles BCA and DAC are alternate interior angles
Hence angle BCA = DAC=60 degree
Angle DAC=60 degree

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ABCD is a cyclic quadrilateral in which BC is parallel to AD, angle ADC = $110^{0}$ and angle BAC = $50^{0}$ . Select the statements that are true.

A B C D

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