Question

ABCD is a kite. If $\angle DAB$ is two times $\angle ADC$, find the value of $\angle ABC$ in terms of $\angle ADC$.

Answer 1

$Let\angle ADC=xThen\angle DAB=2x\angle DAB=\angle DCB\text{(One pair of diagonally opposite angles are equal)}$
$\angle DAB+\angle ABC+\angle BCD+\angle CDA={360}^{\circ }\text{(Angle sum property of a quadrilateral)}2x+\angle ABC+2x+x={360}^{\circ }4x+\angle ABC={360}^{\circ }\angle ABC={360}^{\circ }-4x\angle ABC={360}^{\circ }-4\angle ADC$