question_answer

ABCD is a cyclic trapezium whose sides AD and BC are parallel to each other. If  \[\angle \mathbf{ABC}=\mathbf{7}{{\mathbf{5}}^{{}^\circ }}\], then the measure of the \[\angle \mathbf{BCD}\] is

A)  \[{{162}^{{}^\circ }}\]                      

B)  \[{{18}^{{}^\circ }}\]

C)  \[{{108}^{{}^\circ }}\]                      

D)  \[{{75}^{{}^\circ }}\]

Correct Answer: D

Solution :

(d): \[\angle ABC+\angle DCA={{180}^{{}^\circ }}\] \[\Rightarrow \angle CDA={{180}^{{}^\circ }}-{{75}^{{}^\circ }}={{105}^{{}^\circ }}\] \[AD\parallel BC\] \[\angle BCD=\angle ADE=\angle ABC={{75}^{{}^\circ }}\]