Question

$ABCD$ in a cyclic quadrilateral in which $AB||CD$. If $\angle DAB={115}^o$, determine the measure of $\angle DCB$ and $\angle ABC$.

Answer 1

We have $\angle BAD={180}^{\circ }-\angle DCB$

$⟹\angle DCB={65}^{\circ }$

And now $\angle ABC+\angle BCD={180}^{\circ }$

$⟹\angle ABC={180}^{\circ }-\angle BCD$

$⟹\angle ABC={180}^{\circ }-{65}^{\circ }$

$⟹\angle ABC={115}^{\circ }$