Question

In the given figure, $AB\parallel DC$ and $AD\parallel BC$. If $\angle ABC={75}^{\circ }$, then $\angle CDA$ = ___.

• A. ${105}^{\circ }$
• B. ${30}^{\circ }$
• C. ${75}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is C ${75}^{\circ }$

In $△ABC$ and $△CDA$,

(i) $\angle BAC$ = $\angle DCA$ ....(alternate angles)

(ii) AC = AC .......(common)

(iii) $\angle BCA=\angle DAC$ .....(alternate angles)

$\therefore$ $△ABC\cong △CDA$ .....(ASA Postulate)

$\Rightarrow \angle ABC$ = $\angle CDA$ .......(CPCT)

$\therefore$ If $\angle ABC$ = 75${}^{\circ }$, then $\angle CDA$ = 75${}^{\circ }$.