ABCD is a trapezium in which `AB||DC and angleA=angleB=45^(@)`. Find angles C and D of the trapezium.

Explanation

Given, ABCD is a trapezium and whose parallel sides in the figure are AB and DC.
Since, `AB||CD and BC ` is transversal, then sum of two cointerior angles is `180^(@)`,

`therefore" "angleB+angleC=180^(@)`
`rArr" "angleC=180^(@)-angleB=180^(@)-45^(@)" "[becauseangleB=45^(@)" given"]`
`rArr" "angleC=135^(@)`
Similarly, `" "angleA+angleD=180^(@)" "`[sum of cointerior angles is `180^(@)`]
`rArr" "angleD=180^(@)-45^(@)" "[becauseangleA=45^(@)" given"]`
`rArr" "angleD=135^(@)`
Hence, angles C and D are ` 135^(@)` each.