Aquilt is designed using a square pattern. each square contains two rectangles. each rectangle contains a shaded rhombus. what is the value of x? 50 55 125 145

The value of x is 55 ⇒ 2nd answer

Step-by-step explanation:

* Lets revise the properties of the rhombus

- It has 4 equal sides

- Every two opposite sides are parallel

- Every two opposite angles are equal

- Every two adjacent angles are supplementary (their sum is 180°)

* Now lets solve the problem

- A square divided into two rectangles

- Each rectangle contains a shaded rhombus

- The shaded rhombus has two adjacent angles their measures are

 (2x + 20)° and 50°

∵ Every two adjacent angles in the rhombus are supplementary

∵ The sum of the supplementary angles = 180°

∴ The sum of the measures of the angles (2x + 20)° and 50° is 180°

- lets put the equation and solve it to find x

∴ (2x + 20)° + 50° = 180° ⇒ add the like terms

∴ 2x + 70° = 180° ⇒ subtract 70° from both sides

∴ 2x = 110° ⇒ divide both sides by 2

∴ x = 55°

* The value of x is 55

answer: bearing in mind that a rectangle has a perimeter of length + length + width + width.

step-by-step explanation:

p = perimeter

l = length

x=width

p = 2l + 2x

p = 2(l+x)     < ==== perimeter of the base of the box.