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 \\)
5 multiple choice 4 points
in the accompanying diagram, line \\( a \\) intersects line \\( b \\).
what is the value of \\( x \\) ?
\\( 90 \\)
\\( 10 \\)
\\( 5 \\)
\\( - 10 \\)

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So, \(x + 5=2x - 5\).

Step2: Solve the equation for \(x\)

Subtract \(x\) from both sides: \(5=x - 5\).
Add \(5\) to both sides: \(x=10\).

Answer:

\(10\)