Question

In the given figure, find the value of $\angle$ BAC. Given: $\Delta$DEF is equilateral, $\angle$CBA =40${}^{\circ }$, $\angle$FEC =50${}^{\circ }$ and DE is parallel to BC.

• A. 110⁰
• B. 50⁰
• C. 60⁰
• D. 70⁰

Answer 1

The correct option is D

70⁰

Given: DE$\parallel$BC, so $\angle$ADE =$\angle$DBF= 40${}^{\circ }$(corresponding angle)

$\angle$AED = 180${}^{\circ }$- (50${}^{\circ }$+60${}^{\circ }$) = 70${}^{\circ }$ (Linear pair of angles)

$\angle$AED = $\angle$ECB=70${}^{\circ }$ (Corresponding Angles);

Now consider $\Delta$ADE having $\angle$AED & $\angle$ADE is equal to 70${}^{\circ }$ and 40${}^{\circ }$ respectively.

For determining the $\angle$DAE (or $\angle BAC$) = 180${}^{\circ }$- (70${}^{\circ }$+40${}^{\circ }$) = 70${}^{\circ }$.