Question

in the diagram, \\( \overleftrightarrow { 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 = \\) select choic

Explanation:

Step1: Use the property of perpendicular lines

Since \(\overleftrightarrow{AB}\) and \(\overleftrightarrow{EC}\) are perpendicular, \(\angle CEB = 90^{\circ}\). Also, \(\angle CEB=\angle CEH+\angle HEB\).
So, \(9x+(19x + 6)=90\).

Step2: Solve the equation for \(x\)

Combine like - terms: \(9x+19x+6 = 90\), which simplifies to \(28x+6=90\).
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 \(m\angle HEB = 27^{\circ}\).