Question

The figure shows a rhombus ABCD where the diagonals AC and BD intersect at E. Find the value of x.

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Answer 1

Answer: 2

Explanation:

Using the Z rule, we get the angle of DCE is 2x + 53

The angle DEC is a right angle as the diagonals of a rhombus always make a right angle

So we get the equation

3x + 7 + 2x + 53 + 90 = 180

5x = 10

x = 2

Answer 2

The value of x in the given rhombus is 6.

The sum of the angles in any triangle is 180°.

Triangle DCE.

∠DCE =
`2x + 53,` ( ∠DCE = ∠BAE )

∠DEC = 90°

∠CED =
`3x + 7`

⇒ ∠DCE + ∠DEC + ∠CED =180°

⇒ 2x + 53 + 90 + 3x + 7 = 180°

⇒ 5x + 150 = 180

⇒ 5x = 30

x = 6.

Therefore, the correct value of x is 6.