Question

The internal bisectors of $\angle Q$ and $\angle R$ of $△PQR$ meet at C. If $\angle P={70}^{\circ }$, then $\angle QCR$ is:

• A. ${110}^{\circ }$
• B. ${125}^{\circ }$
• C. ${130}^{\circ }$
• D. ${140}^{\circ }$

Answer 1

The correct option is B ${125}^{\circ }$

Let $\angle PQR=2x$ and $\angle PRQ=2y$
From $△PQR$
$2x+{70}^{\circ }+2y={180}^{\circ }$
or $2(x+y)={110}^{\circ }$
or $x+y={55}^{\circ }$ ...(i)
Also, from $△QCR$
$x+\angle QCR+y={180}^{\circ }$
or $(x+y)+\angle QCR={180}^{\circ }$
From equation (i), we get
${55}^{\circ }+\angle QCR={180}^{\circ }$
or $\angle QCR={125}^{\circ }$