In the given congruent triangles under ASA, find the value of x and y, ΔPQR = ΔSTU.

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$x = 30^{o}, y = 90^{o}$

$x = 30^{o}, y = 30^{o}$

$x = 70^{o}, y = 70^{o}$

$x = 90^{o}, y = 90^{o}$

answer is A.

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Detailed Solution

Given: ΔPQR = ΔSTU (By ASA rule)
∠Q = ∠T = 60° (given)
QR = TU = 4 cm (given)
∠x = 30° (for ASA rule)
Now in ΔSTU,
∠S + ∠T + ∠U = 180° (Angle sum property)
∠y + 60° + ∠x = 180°
∠y + 60° + 30° = 180°
∠y + 90° = 180°
∠y = 180° – 90° = 90°
Hence, x = 30° and y = 90°.

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