Question

Find the measure of $\angle$PQR, if $\angle$ZXY = 25°.

Answer 1

Given, in triangles, $△$PQR and $△$XYZ,
side RP = side ZX = 6 cm
$\angle$QRP = $\angle$YZX = 140°
side QR = side YZ = 9 cm

$\therefore$ by SAS criterion for congruency of triangles, $△$PQR $\cong △$XYZ

So,
$\angle$RQP = $\angle$ZXY = 25° (corresponding parts)

In triangle, $△$PQR,
$\angle$PQR = 180° - ($\angle$RQP + $\angle$QRP)
$\Rightarrow$ $\angle$PQR = 180° - (25° + 140°)
$\Rightarrow$ $\angle$PQR = 15°