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Reptile [31]
4 years ago
7

Someone, please help I have a time limit

Mathematics
1 answer:
VladimirAG [237]4 years ago
6 0

(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°

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