Question

geometry ic sem b classifying quadrilaterals what is the value of x? 18 10 2y + 4 10 + 2x 8 6 3

Explanation:

Step1: Use property of rectangle

In a rectangle, opposite - sides are equal. The given quadrilateral is a rectangle (since all angles are right - angles). So, we can set up an equation for the opposite sides. The two horizontal sides are equal, so \(18=10 + 2x\).

Step2: Solve the equation for \(x\)

Subtract 10 from both sides of the equation \(18=10 + 2x\). We get \(18−10=2x\), which simplifies to \(8 = 2x\). Then divide both sides by 2: \(\frac{8}{2}=x\), so \(x = 4\). But this is wrong. Let's use the other pair of opposite sides. The two vertical sides are equal, so \(10=2y + 4\). Solving for \(y\) gives \(2y=10 - 4=6\), \(y = 3\). Now, using the horizontal sides equation \(18=10 + 2x\), we solve as follows:
Subtract 10 from both sides: \(18-10=2x\), so \(8 = 2x\).
Divide both sides by 2: \(x = 4\).

Answer:

4