Question

Someone, please help I have a time limit

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°