Question

4
multiple choice 4 points
in the accompanying diagram, \\( \overrightarrow { b d } \perp \overleftrightarrow { a b c } \\) at \\( b \\) and \\( \overrightarrow { b e } \perp \overrightarrow { b f } \\) at \\( b \\). if \\( m \angle f b c = 20 \\),
what is \\( m \angle e b d \\) ?
70
110
20
90

Explanation:

Step1: Determine \(m\angle DBF\)

Since \(\overrightarrow{BD}\perp\overrightarrow{ABC}\), \(m\angle DBC = 90^{\circ}\). Given \(m\angle FBC=20^{\circ}\), then \(m\angle DBF=m\angle DBC - m\angle FBC\).
\(m\angle DBF = 90^{\circ}- 20^{\circ}=70^{\circ}\)

Step2: Determine \(m\angle EBD\)

Since \(\overrightarrow{BE}\perp\overrightarrow{BF}\), \(m\angle EBF = 90^{\circ}\). We know that \(m\angle EBF=m\angle EBD + m\angle DBF\). So \(m\angle EBD=m\angle EBF - m\angle DBF\)
Substitute \(m\angle EBF = 90^{\circ}\) and \(m\angle DBF = 70^{\circ}\) into the formula: \(m\angle EBD=90^{\circ}-70^{\circ} = 20^{\circ}\)

Answer:

\(20\)