Questions: A quilt is designed using a square pattern. Each square contains two rectangles. Each rectangle contains a shaded rhombus. What is the value of x ?

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

What is the value of x ?

Transcript text: A quilt is designed using a square pattern. Each square contains two rectangles. Each rectangle contains a shaded rhombus. What is the value of $x$ ?

Solution

Solution Steps

Step 1: Identify the properties of a rhombus.

A rhombus has four equal sides, and opposite angles are equal. Adjacent angles in a rhombus are supplementary (they add up to 180°).

Step 2: Set up an equation.

Since adjacent angles are supplementary, we know that 50° + (2x + 20)° = 180°.

Step 3: Solve for x.

Simplify the equation: 2x + 70 = 180 Subtract 70 from both sides: 2x = 110 Divide both sides by 2: x = 55

Final Answer

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