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In a Rhombus Abcd, If ∠Acb = 40°, Then ∠Adb = - Mathematics

MCQ

In a rhombus ABCD, if ∠ACB = 40°, then ∠ADB =

Options

  •  70°

  • 45°

  • 50°

  • 60°

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Solution

Rhombus ABCD is given as follows:

It is given that∠ACB = 40°.

Therefore, ∠OCB = 40° (Because O lies on AC)

We know that the diagonals of a rhombus intersect at right angle.

Therefore, ∠BOC = 90°

By angle sum property of a triangle, we get:

∠CBO + ∠OCB + ∠BOC = 180°

        ∠CBO + 40° + 90° = 180°

                ∠CBO+ 130° = 180 °

                          ∠CBO = 50°

Since, O lies on BD

 ∠CBD = 50°

Also , CB || DA

Therefore,

∠ADB = ∠CBD

 ∠ADB = 50°

Hence, the correct choice is (c).

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Mathematics for Class 9
Chapter 13 Quadrilaterals
Q 23 | Page 72
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