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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