If AB||CD and CD||EF Find $\angle$ACE
"
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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