Question

ABCD is a rhombus, where m∠AED = 5x – 10. Use the properties of a rhombus to determine the value of x.

A) x = 5

B) x = –2

C) x = 20

D) x = 16

Answer 1

B) x = –2

Explanation:

5x - 10 + 180 = 180.

7. Simplify further to 5x + 170 = 180.

8. Solve for x by subtracting 170 from both sides: 5x = 10.

9. Divide both sides by 5: x = 2.

Answer 2

C) x = 20

Explanation:

Since ABCD is a rhombus, we know that the diagonals of ABCD bisect each other at right angles.

This means that:

m ∠ AED = 90°

We are also given that m∠AED = 5x – 10.

Setting these two equations equal to each other, we get:

5x - 10 = 90

Add 10 on both sides:

5x - 10 + 10= 90 + 10

5x = 100

Divide both sides by 5.

`\sf (5x)/(5)=(100)/(5)`

x = 20

Therefore, the value of x is 20.