If AB||CD and CD||EF Find $\angle$ACE
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Given: If AB||CD and CD||EF 

To find: Find $\angle$ACE

Solution:

EF   and   CD  are parallel  ;  CE  is a transversal pass through the parallel lines  EF   and   CD

Sum of angles in same side of transversal which passes through parallel lines  is  180°  

$\angle$DCE  $+$  angle  CEF   =  180°  

$\angle$ DCE  $+$  130°   =  180°

$\angle$DCE   =  180°  $-$   130°

$\angle$DCE   =  50°

AB  is parallel to CD

$\angle$BAC  and $\angle$ ACD  are alternate interior angles.

So,  angle  BAC   =  $\angle$ACD 

70°   =  $\angle$ACD 

$\angle$ACD   =  70°

$\angle$ACD   =  angle DCE  $+$  angle ACE 

$\angle$ DCE   =  50°

70°  =  50°  $+$   angle ACE

Rewrite,

 50°  $+$  $\angle$ ACE  =  70°

$\angle$ ACE  =  70°  $-$   50°

 $\angle$ACE  =   20°

Therefore the measure of  $\angle$ACE is 20°

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Updated on: 10-Oct-2022

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