Question

Someone, please help I have a time limit

1, ABCD is a rhombus. Find the value of x. Show your work.
2. ABCD is a rhombus. What is x? Show your work.
3. ABCD is a rhombus. What is x?

Answer 1

(1) x° = 38° (2) x° = 54° (3) x° = 4°

Step-by -step explanation:

(1) Given ABCD is a rhombus.

Let us take a triangle AED.

Diagonals are perpendicular in rhombus – – – (i)

`\angle \mathrm{AED}=90^(\circ)`

Sum of the adjacent angles in a triangle is 180°.

`\angle \mathrm{EAD}+\angle \mathrm{ADE}+\angle \mathrm{AED}=180^(\circ)`

⇒ x° + (x + 14)° + 90° = 180°

⇒ 2x° = 76°

⇒ x° = 38°

(2) Given ABCD is a rhombus,
`\angle \mathrm{CED}=90^(\circ)` (by (i))

`\angle \mathrm{CDE}+\angle \mathrm{DCE}+\angle \mathrm{CED}=180^(\circ)`

⇒ x° + (x – 18)° + 90° = 180°

⇒ 2x° = 108°

⇒ x° = 54°

(3) Given ABCD is a rhombus.

BD bisect the angle
`\angle \mathrm{ADC}`.

⇒ 8x° = 32

⇒ x° = 4°