Question

Given that ABCD is a rhombus, find the value of x.

Answer 1

Answer:

C

Step-by-step explanation:

The diagonals of a rhombus are perpendicular bisectors of each other.

Thus the angle at the intersection of the diagonals is 90°

The sum of the 3 angles in a triangle = 180°

Sum the angles in the lower triangle and equate to 180, that is

90 + x + x + 40 = 180

2x + 130 = 180 ( subtract 130 from both sides )

2x = 50 ( divide both sides by 2 )

x = 25 → C

Answer 2

The value of x is 25.

What are some of the properties of a rhombus?

• All four sides are equal.
• Diagonals bisect each other at 90°.

Given

ABCD is a rhombus,

∠CAD = x°,

∠BDA = (x + 40)°.

Find the equation in x

Let the point where the diagonals intersect be E.

Then, using the property of the rhombus ∠AED = 90°.

We know, in a triangle that the sum of all the three interior angles equals 180°. So, we get,

     ∠AED + ∠BDA + ∠CAD = 180°

⇒                 ∠BDA + ∠CAD = 180° - ∠AED

                                                = 180° - 90° = 90°      (∠AED = 90°)

Put the given values of these angles,

          (x + 40)° + x° = 90°.

This is the equation to be solved to obtain x.  

Solve for x  

           (x + 40)° + x° = 90°

⇒   (2x)° = 90° - 40° = 50°

⇒         x° = (50 / 2)°

⇒         x = 25.

The required value of x is 25.

Learn more about the properties of a rhombus here

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