question_answer

The side AC of a\[\Delta ABC\]is extended to D such That\[BC=CD.\] If \[\angle ACB\]is \[70{}^\circ ,\]then \[\angle ADB\]is equal to

A) \[35{}^\circ \]  

B) \[45{}^\circ \]

C) \[70{}^\circ \]                          

D) \[110{}^\circ \]

Correct Answer: A

Solution :

\[\angle ACB+\angle BCD=180{}^\circ \]            [linear pair]

\[\angle BCD=180{}^\circ -70{}^\circ =110{}^\circ \]

In \[\Delta BCD,\]           \[BC=CD\]

\[\angle CBD=\angle CDB\]         ... (i)

[angles opposite to equal sides]

Also, \[\angle BCD+\angle CBD+\angle CDB=180{}^\circ \]

\[2\angle CDB=180{}^\circ -\angle BCD\]

\[=180{}^\circ -110{}^\circ =70{}^\circ \]

\[\therefore \]      \[\angle CDB=\angle ADB=\frac{70{}^\circ }{2}=35{}^\circ \]