In the given figure, find the value of ∠BAC. ΔDEF is equilateral, ∠CBA=40∘, ∠FEC=50∘ and DE is parallel to BC. [4 MARKS]
Steps: 3 Marks
Result: 1 Mark
Given DE∥BC,∠CBA=40∘
⇒∠ADE=∠CBA=40∘ [corresponding angle]
Since, ΔDEF is equilateral
⇒∠DEF=60∘
∠FEC=50∘ (Given)
∠AED=180∘−(50∘+60∘) (Angles on a straight line)
= 70∘
Consider ΔADE ,
∠AED=70∘ & ∠ADE=40∘
∠ADE+∠AED+∠DAE=180∘ [Angle sum property]
⇒∠DAE=180∘−(70∘+40∘)=70∘.
∴∠BAC=∠DAE=70∘.