Question

A quilt is designed using a square pattern. Each square contains two rectangles. Each rectangle contains a shaded rhombus.

Answer 1

The sum of angles in any Rhombus is 360 degrees.Opposite angles of a rhombus are congruent.

Two of the adjacent angles are 2x+20 and 50 degrees.

The opposite angles measure 2x+20 and 50 degrees.

Sum of angles in any Rectangle is 360

2x+20+50+2x+20+50=360

Adding line terms,

4x+140=360

Subtracting 140 both sides:

4x=220

Dividing both sides by 4

x=55

Option B. 55  is the right answer.

Answer 2

The 4 angles of a rhombus should add up to be 360 degrees.

So,........................... 2x + 20 + 2x + 20 + 50 +50 = 360

Combine like terms:............................... 4x + 140 = 360

Subtract 140 from both sides ..........................4x = 220

Divide by 4..............................................................  x = 55