Question

1. if \\( \overline { b d } \perp \overline { a c } \\), \\( m \angle d b e = ( 2 x - 1 ) ^ { \circ } \\), and \\( m \angle c b e = ( 5 x - 42 ) ^ { \circ } \\), find the value of \\( x \\).

Explanation:

Step1: Use perpendicular property

Since \( \overline{BD}\perp\overline{AC} \), \( \angle CBD = 90^{\circ} \). And \( \angle CBE=\angle CBD+\angle DBE \). So \( (5x - 42)^{\circ}=(2x - 1)^{\circ}+90^{\circ} \).

Step2: Solve the equation

$$
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$$

Answer:

\( x = 19 \)