Question

AB is the shortest and CD is the longest side of the quadrilateral ABCD as shown in the following figure, prove that $\angle A>\angle C$.

Answer 1

Consider $\Delta ACD$

$\because CD$ is loyent side

$\angle CAD>\angle ACD$ ___ (1)

Consider $\Delta ACB$

$\because AB$ is smaller side

$\angle CAB>\angle ACB$ ___ (2)

Adding (1) & (2)

$\angle A>\angle C$