Question

$RA$ is the bisector of an angle of equilateral triangle $PQR$, then $\angle ARQ=$

• A. ${30}^{\circ }$
• B. ${45}^{\circ }$
• C. ${20}^{\circ }$

Answer 1

The correct option is A ${30}^{\circ }$

$PQR$ is an equilateral triangle.
$\Rightarrow \angle P=\angle Q=\angle R={60}^{\circ }$
Now, By S - S - S congruency:
$\Delta RAP\cong \Delta RAQ$
$\Rightarrow ARP=\angle ARQ$
Also, we know $\angle R={60}^{\circ }$
$\Rightarrow \angle ARP+\angle ARQ=\angle R={60}^{\circ }$
$\Rightarrow 2\times \angle ARQ={60}^{\circ }$
$\Rightarrow \angle ARQ={30}^{\circ }$