Question

selected response: 1 point for answer only. examine the figure. select color select size eraser figure is not drawn to scale. if $\triangle abc \cong \triangle def$, determine the value of $x$ $\circ$ $x = 24$ $\circ$ $x = 27$ $\circ$ $x = 31$ $\circ$ $x = 39$

Explanation:

Step1: Use the property of congruent triangles

Since \(\triangle ABC\cong\triangle DEF\), their corresponding sides are equal. So \(AC = DF\).

Step2: Set up the equation

We know \(AC=2(x + 3)\) and \(DF=(4x-42)\). Then \(2(x + 3)=4x-42\).

Step3: Expand the left - hand side

Using the distributive property \(a(b + c)=ab+ac\), we get \(2x+6 = 4x-42\).

Step4: Move the \(x\) terms to one side

Subtract \(2x\) from both sides: \(2x+6-2x=4x - 42-2x\), which simplifies to \(6 = 2x-42\).

Step5: Solve for \(x\)

Add \(42\) to both sides: \(6 + 42=2x-42 + 42\), so \(48 = 2x\). Then divide both sides by \(2\): \(x=\frac{48}{2}=24\).

Answer:

\(x = 24\)