Question

in the accompanying diagram, lines \\( \overleftrightarrow { a b } \\) and \\( \overleftrightarrow { c d } \\) intersect at point \\( e \\). if \\( m \angle a e d = ( x + 10 ) \\) and \\( m \angle c e b = 50 \\), find \\( x \\).

Explanation:

Step1: Use vertical angles property

Vertical angles are equal. So, \(m\angle AED=m\angle CEB\).

Step2: Set up the equation

Since \(m\angle AED=(x + 10)\) and \(m\angle CEB = 50\), we have \(x+10=50\).

Step3: Solve for \(x\)

Subtract \(10\) from both sides of the equation: \(x=50 - 10\).

Answer:

\(40\)