Mathematics

In figure, side BC to $$\Delta$$ABC has been produced to D and CE$$||$$BA. If $$\angle ABC=65^o$$, $$\angle BAC=55^o$$, find $$\angle ACE, \angle ECD$$ and $$\angle ACD$$.


SOLUTION
$$\angle ABC=65^o$$ and $$\angle BAC=55^o$$
$$line\ AB\ ||\ line\ CE $$
$$\therefore$$ $$\angle ABC$$ and $$\angle ECD$$ are corresponding angles.
Corresponding angles formed by parallel lines are congruent.
$$\therefore \angle ABC=\angle ECD$$
$$\therefore \angle ECD=65^0$$

Also, $$\angle BAC$$ and $$\angle ACE$$ are alternate angles .
Alternate angles formed by parallel lines are congruent.
$$\therefore \angle BAC=\angle ACE$$
$$\therefore\angle ACE=55^0$$
Now, 
$$\angle ACD=\angle ACE+\angle ECD$$          ....$$\{adjacent\  angles\}$$
$$\therefore \angle ACD=65^0+55^0$$  
$$\therefore \angle ACD=120^0$$  

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Subjective Medium Published on 09th 09, 2020
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