1.

In the given figure, PQRS is a rectangle. If ∠RPQ = 30° then find the value of (x + y).

Answer»

Since, diagonal of a rectangle are equal and bisect each other and vice versa.

OR = OS

⇒ ∠ORS = ∠OSR …(i)

Also PQ || SR

⇒ ∠OPQ = ∠ORS = 30° …(ii) (alt. angles)

In ΔORS,

∠ORS + ∠OSR + y = 180° (angle sum property)

⇒ 30° + 30° + y = 180° [using (i) and (ii)]

⇒ y = 120°

Also OR = OQ

⇒ ∠ORQ = ∠OQR = x

In ΔORQ,

x + x + ∠ROQ = 180°

⇒ 2x + 60° = 180° (∵ y + ∠ROQ = 180° i.e. linear pair of angles)

⇒ x = \(\frac { 120 }{ 2 }\) = 60°

x + y = 60° + 120° = 180°


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