1.

ABCD is a rectangle. Find \(x\).(a) 54° (b) 36°(c) 24° (d) 18°

Answer»

(d) 18°

Diagonals of a rectangle are equal and bisect each other. 

∴ In ΔAOB ,∠AOB = 162° – 3\(x\)        (vert. opp. ∠s) 

∠OBA =∠OAB = 2x (∵OA = OB) 

∴ ∠AOB +∠OBA+∠OAB = 180° 

⇒ 162°– 3\(x\) + 2\(x\) + 2\(x\) = 180° ⇒ \(x\) = 18°



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