In the adjoining figure, ABCD is a quadrilateral in which AB is the longest side and CD is the shortest side.
Prove that (i) `angle C gt angle A, " (ii) "angle D gt angle B.`

Explanation

Join AC and BD.
In `triangle ABC, AB gt BC rArr angle ACB gt angleBAC.`
In `triangle ADC, AD gt DC rArr angle ACD gt angle CAD`
` " " `[`because` in a triangle, the longer side has the greater angle opposite it].
`therefore angle ACB +angle ACD gt angle BAC+ angle CAD.`
`therefore angle C gt angle A. `
Similarly, `angle D gt angle B.`