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प्रश्न
PQRS is a rectangle. Find the angles marked x and y.
बेरीज
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उत्तर
Given, PQRS is a rectangle.
In a rectangle, opposite sides are parallel.
Angles opposite to equal sides are equal in a triangle.
∠PQO = 24°
In a rectangle, diagonals are equal and they bisect each other.
Let PR and QS meet at O.
So, we have, OR = OQ
⇒ ∠ORQ = 24°
All interior angles of a rectangle are right angles.
⇒ y + ∠OQR = 90° ...(∵ ∠RQP = 90°)
⇒ y = 90° – 24° = 66°
We know that the sum of the interior angle of a triangle = 180°
⇒ 24° + x + 24° = 180°
⇒ x = 180° – 48° = 132°
Hence, this is required.
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