question_answer

\[\mathbf{AB}\parallel \mathbf{CD},\angle \mathbf{ABO}=\mathbf{12}{{\mathbf{8}}^{{}^\circ }},\angle \mathbf{BOD}=\mathbf{14}{{\mathbf{2}}^{{}^\circ }}\], Then, \[\angle \mathbf{ODC}\] = ?

A)  \[{{100}^{{}^\circ }}\]                     

B)  \[{{80}^{{}^\circ }}\]

C)  \[{{90}^{{}^\circ }}\]  

D)  \[{{88}^{{}^\circ }}\]

Correct Answer: C

Solution :

(c): \[\angle ABO={{128}^{{}^\circ }}\] \[\therefore \]\[MBO={{180}^{{}^\circ }}-{{128}^{{}^\circ }}={{52}^{{}^\circ }}\] \[\therefore \]\[\angle MOD={{142}^{{}^\circ }}-{{52}^{{}^\circ }}={{90}^{{}^\circ }}\] \[\therefore \]\[\angle ODC={{180}^{{}^\circ }}-{{90}^{{}^\circ }}={{90}^{{}^\circ }}\]