Question

ABCD is a rhombus, where m∠AED = 5x – 10. Use the properties of a rhombus to determine the value of x. ANSWERS: A) x = 20 B) x = 5 C) x = 16 D) x = –2

Answer 1

A) x = 20

Explanation:

ABCD is a rhombus, AC and BD are diagonals which intersect each other at point E.

Since, diagonals of a rhombus are perpendicular bisector.

`\therefore \: m \angle AED = 90 \degree \\ \therefore \: (5x - 10) \degree = 90 \degree \\ \therefore \: 5x - 10 = 90 \\ \therefore \: 5x = 90 + 10 \\ \therefore \: 5x = 100 \\ \\ \therefore \: x = (100)/(5) \\ \\ \huge \red{ \boxed{ \therefore \: x =20}}`