Question

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

Explanation:

Step1: Recall perpendicular - angle property

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

Step2: Combine like - terms

Combine the $x$ terms: $19x+9x+6 = 90$, which simplifies to $28x+6 = 90$.

Step3: Isolate the variable term

Subtract 6 from both sides of the equation: $28x=90 - 6$, so $28x=84$.

Step4: Solve for $x$

Divide both sides by 28: $x=\frac{84}{28}=3$.

Step5: Find $m\angle HEB$

Substitute $x = 3$ into the expression for $m\angle HEB$. Since $m\angle HEB=(9x)^{\circ}$, then $m\angle HEB=9\times3 = 27^{\circ}$.

Answer:

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