Question

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

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

Answer 1

Answer: (B)

${125}^o$

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