ABCD is a rectangle. If ∠BPC = 124°, calculate : (i) ∠BAP (ii) ∠ADP.

Question

KnowledgeBoat · Accepted Answer

Since ABCD is a rectangle, the diagonals bisect each other, and ∠BPC forms two angles at point P. According to the properties of a rectangle, the diagonals are equal and intersect at the midpoint. (i) ∠BAP = of ∠BPC (since diagonals bisect each other). So, ∠BAP = × 124° = 62°. Hence, the value of ∠BAP is 62°. (ii) Diagonals of rectangle are equal and bisect each other. ⇒ ∠PBC = ∠PCB = x (say) But, in triangle BPC, sum of all the angles are 180°. ⇒ ∠BPC \+ ∠PBC \+ ∠PCB = 180° ⇒ 124° \+ x \+ x = 180° ⇒ 2x = 180° − 124° ⇒ 2x = 56° ⇒ x = 28° ⇒ ∠PBC = 28° But ∠PBC = ∠ADP [alternate angles] ∠ADP = 28° Hence, the value of ∠ADP is 28°.

Mathematics

ABCD is a rectangle. If ∠BPC = 124°, calculate :
(i) ∠BAP
(ii) ∠ADP.

Quadrilaterals

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Mathematics

ABCD is a rectangle. If ∠BPC = 124°, calculate :(i) ∠BAP(ii) ∠ADP.