Question

solve for x. figures are not necessarily drawn to scale. answer attempt 1 out of 2 x = submit answer

Explanation:

Step1: Use the similarity of triangles

Since \(\angle F = \angle C=97^{\circ}\) and \(\angle GEF=\angle DEC\) (vertically - opposite angles), \(\triangle GEF\sim\triangle DEC\) (by the AA - Angle - Angle similarity criterion).
For similar triangles, the ratios of corresponding sides are equal. So, \(\frac{GE}{DE}=\frac{GF}{DC}\).
We know that \(GE = 35\), \(DE = 56\), \(DC = 40\), and \(GF=x\).

Step2: Substitute values into the proportion

Substituting the values into the proportion \(\frac{35}{56}=\frac{x}{40}\).
Cross - multiply: \(56x=35\times40\).
First, calculate \(35\times40 = 1400\). Then, \(x=\frac{1400}{56}\).
Simplify \(\frac{1400}{56}=\frac{1400\div28}{56\div28}=\frac{50}{2} = 25\).

Answer:

\(25\)