Question

in the diagram, \\( \overrightarrow { a b } \\) and \\( \overrightarrow { e c } \\) are perpendicular.

if \\( m \angle h e b = ( 9 x ) ^ { \circ } \\) and \\( m \angle c e h = ( 19 x + 6 ) ^ { \circ } \\), then the value of \\( x \\) is select choice and \\( m \angle h e b = \\)

Explanation:

Step1: Use perpendicular property

Since \(\overrightarrow{AB}\) and \(\overrightarrow{EC}\) are perpendicular, \(\angle CEB = 90^{\circ}\). So \(m\angle HEB+m\angle CEH = 90^{\circ}\).
Given \(m\angle HEB=(9x)^{\circ}\) and \(m\angle CEH=(19x + 6)^{\circ}\), we have the equation \(9x+19x + 6=90\).

Step2: Solve the equation

Combine like - terms: \(28x+6 = 90\).
Subtract 6 from both sides: \(28x=90 - 6=84\).
Divide both sides by 28: \(x=\frac{84}{28}=3\).

Step3: Find \(m\angle HEB\)

Substitute \(x = 3\) into \(m\angle HEB=(9x)^{\circ}\). Then \(m\angle HEB=9\times3=27^{\circ}\).

Answer:

The value of \(x\) is \(3\) and \(m\angle HEB = 27^{\circ}\)