Question

solve for ( x ). figures are not necessarily drawn to scale.

Explanation:

Step1: Identify Similar Triangles

Triangles \( \triangle FGE \) and \( \triangle DCE \) are similar because \( \angle F = \angle C = 49^\circ \) and \( \angle FEG = \angle DEC \) (vertical angles). So, their corresponding sides are proportional.

Step2: Set Up Proportion

The ratio of \( FG \) to \( DC \) should equal the ratio of \( GE \) to \( DE \). So, \( \frac{FG}{DC} = \frac{GE}{DE} \). Substituting the known values: \( FG = 10 \), \( DC = 25 \), \( DE = 30 \), and \( GE = x \). So, \( \frac{10}{25} = \frac{x}{30} \).

Step3: Solve for \( x \)

Cross - multiply: \( 25x = 10\times30 \). Then, \( 25x = 300 \). Divide both sides by 25: \( x=\frac{300}{25}=12 \).

Answer:

\( x = 12 \)