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

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Solution

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

$∴$ by SAS criterion for congruency of triangles, $△$ PQR $≅ △$ XYZ

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

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

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