Question

The value of $\angle BAC$ is

• A. ${35}^{\circ }$
• B. ${65}^{\circ }$
• C. ${75}^{\circ }$
• D. ${85}^{\circ }$

Answer 1

Answer: (C)

${75}^{\circ }$

$\Rightarrow$ Draw a line segment $PQ=AB+BC+CA=9.8cm.$

$\Rightarrow$ Make $\angle LPQ={45}^o$ and $\angle MQP={60}^o$

$\Rightarrow$ Now bisect $\angle LPQ$ and $\angle MQP$ such that their bisectors meet at $A.$

$\Rightarrow$ Draw perpendicular bisector of $AP$ and $AQ$ i.e.

$XY$ and $ST$ intersecting $PQ$ at $B$ and $C$ respectively.

$\Rightarrow$ Join $AB$ and $AC$

$\Rightarrow$ Now, measure the $\angle BAC$

$\Rightarrow$ We get, $\angle BAC={75}^o$.