question_answer

In the adjoining figure, A \[A\mathbf{B}\parallel \mathbf{DE}.\]\[\angle \mathbf{ABC}=\mathbf{5}{{\mathbf{7}}^{{}^\circ }}\]and\[\angle \mathbf{EDC}=\mathbf{3}{{\mathbf{3}}^{{}^\circ }}.\]Find\[\angle \mathbf{BCD}\]

A)  \[{{90}^{{}^\circ }}\]  

B)  \[{{50}^{{}^\circ }}\]

C)  \[{{80}^{{}^\circ }}\]                                   

D)  \[{{105}^{{}^\circ }}\]

Correct Answer: A

Solution :

(a): \[\angle BCD=\angle BCM+\angle DCM\] \[=\angle ABC+\angle EDC={{57}^{{}^\circ }}+{{33}^{{}^\circ }}={{90}^{{}^\circ }}\]