Question

Abcd is a rhombus in which ab ac find all the angles of the rhombus

Answer 1

ABCD is a Rhombus ⇒ AC = BC ------------ (1) [Given data] BC = AB --------------- (2) [Sides of the Rhombus] From equations (1) and (2) AC = BC = AB

⇒ ΔABC is an equilateral triangle.

So, <ABC = 60°, <BCA = 60° ------------------------- (3) <CAB = 60° --------------------------(4) Similarly, in ΔADC, AD = DC [Sides of a rhombus] AD = BC But BC = AC

∴ AD = AC

∴ AD = DC = AC

∴ DADC is an equilateral triangle.

⇒ <CAD = 60° ---------------- (5)

⇒ <ADC = 60°

⇒ <DCA = 60° ----------------- (6)

From equations (3) and (6), we get <BCA + <DCA = 60° + 60° = 120°

∴ <C = 120°

From equations (4) and (5), <CAB + <CAD = 60° + 60° = 120° <A = 120°. Therefore, four angles of the rhombus are 120°, 60°, 120°, 60°.

Answer 2

Answer:

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