Question

in the diagram, ab and ec are perpendicular. if (mangle heb=(9x)^{circ}) and (mangle ceh=(19x + 6)^{circ}), then the value of x is and (mangle heb=)

Explanation:

Step1: Use perpendicular - angle property

$m\angle HEB+m\angle CEH = 90^{\circ}$
$9x+(19x + 6)=90$

Step2: Combine like - terms

$28x+6 = 90$
$28x=90 - 6$
$28x=84$

Step3: Solve for x

$x=\frac{84}{28}=3$

Step4: Find $m\angle HEB$

$m\angle HEB=9x=9\times3 = 27^{\circ}$

Answer:

$x = 3$, $m\angle HEB=27^{\circ}$