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SAS Similarity

What will be ...

Question

What will be the measure of $∠$ PQR,
if $∠$ ZXY = 25° ?

25°

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15°

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35°

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10°

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Solution

The correct option is B 15°
Given, in triangles, $△$ PQR and $△$ XYZ,
side RP = side ZX = 6cm
$∠$ QRP = $∠$ YZX = 140°
side QR = side YZ = 9cm

$∴$ 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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Class:	$5 - 10$	$10 - 15$	$15 - 20$	$20 - 25$	$25 - 30$	$30 - 35$	$35 - 40$	$40 - 45$
Frequency:	$5$	$6$	$15$	$10$	$5$	$4$	$2$	$2$

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