Question

1. find the value of x.

Explanation:

Step1: Find angle in triangle \(ABC\)

In right - triangle \(ABC\), \(\angle B = 90^{\circ}\), \(\angle C=65^{\circ}\). Using the angle - sum property of a triangle (\(\angle A+\angle B+\angle C = 180^{\circ}\)), we find \(\angle BAC=180^{\circ}-90^{\circ}-65^{\circ}=25^{\circ}\).

Step2: Use parallel line property (if \(AB\parallel DE\))

Assume \(AB\parallel DE\) (implied by the figure's right - angle structure). Then \(AC\parallel DF\) (by the nature of the figure's construction). So, \(\angle BAC=\angle DFE\) (alternate interior angles for parallel lines \(AC\) and \(DF\)).

Answer:

\(x = 25\)