Question

Referring the figure given below, for $\Delta PQR$ and $\Delta XYZ$, $PQ=YZ,QR=XZ$ and $\angle Q=\angle Z$. The value of $\angle P$ is ___.

• A. ${42}^{\circ }$
• B. ${75}^{\circ }$
• C. ${63}^{\circ }$
• D. Cannot be determined

Answer 1

Answer: (A)

${42}^{\circ }$

For $\Delta PQR$ and $\Delta XYZ,$
$PQ=YZ$
$QR=XZ$
$\angle Q=\angle Z$
$\therefore \Delta PQR\cong \Delta XYZ$ ($S.A.S.$ condition for congruence)
$\therefore \angle R=\angle X={63}^o$
$\angle P=\angle Y$
$\angle Q=\angle Z={75}^o$
Now, $\angle P+\angle Q+\angle R={180}^o$
$\therefore \angle P+{75}^o+{63}^o={180}^o$
$\angle P={42}^o.$