ABCD is a rhombus in which the altitude from D to side AB bisects AB. Then angle A and angle B are respectively ____ & ____.

(pls answer with explanation)

Given : ABCD is a rhombus. DE is the altitude on AB such that AE = EB.

In ΔAED and ΔBED,

DE = DE (Common side)

∠DEA = ∠DEB (90°)

AE = EB (Given)

∴ ΔAED ΔBED ( SAS congruence rule)

⇒ AD = BD (C.P.C.T.)

Also, AD = AB [Sides of rhombus are equal]

⇒ AD = AB = BD

Thus, ΔABD is an equilateral triangle.

∴ ∠A = 60°

⇒ ∠C = ∠A = 60° [Opposite angles of rhombus are equal]

∠ABC + ∠BCD = 180° [Sum of adjacent angles of a rhombus is supplementary]

∴∠ABC + 60° = 180°

⇒ ∠ABC = 180° – 60°

⇒ ∠ABC = 120°

∴ ∠ADC = ∠ABC = 120° [Opposite angles of a rhombus are equal]

Thus, angles of rhombus are 60°, 120°, 60° and 120°.

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