Question

If $\angle$ACD = 120${}^{\circ }$ and $\angle$B = 20${}^{\circ }$, what is the value of $\angle$BAC?

• A. 120${}^{\circ }$
• B. 140${}^{\circ }$
• C. 100${}^{\circ }$
• D. 160${}^{\circ }$

Answer 1

The correct option is C 100${}^{\circ }$

$\because$ $\angle$ACB + $\angle$ACD = 180${}^{\circ }$
$\angle$ACB = 180${}^{\circ }$- $\angle$ACD
$\Rightarrow$ $\angle$ACB = 180${}^{\circ }$ - 120${}^{\circ }$
$\Rightarrow$ $\angle$ACB = 60${}^{\circ }$
In $△$ABC,
$\angle$BAC + $\angle$ABC + $\angle$ACB = 180${}^{\circ }$
$\Rightarrow$ $\angle$BAC + 20${}^{\circ }$ + 60${}^{\circ }$ = 180${}^{\circ }$
$\Rightarrow$ $\angle$BAC = 100${}^{\circ }$