Question

in the diagram, $overleftrightarrow{ab}$ and $overrightarrow{ec}$ are perpendicular. if $mangle heb=(9x)^{circ}$ and $mangle ceh=(13x + 2)^{circ}$, 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 $\angle CEB=\angle CEH+\angle HEB$.

Step2: Set up the equation

We know that $m\angle HEB=(9x)^{\circ}$ and $m\angle CEH=(13x + 2)^{\circ}$, so $(13x + 2)+9x=90$.

Step3: Combine like - terms

$13x+9x+2 = 90$, which simplifies to $22x+2 = 90$.

Step4: Solve for $x$

Subtract 2 from both sides: $22x=90 - 2=88$. Then divide both sides by 22: $x=\frac{88}{22}=4$.

Step5: Find $m\angle HEB$

Substitute $x = 4$ into the expression for $m\angle HEB$. $m\angle HEB=9x$, so $m\angle HEB=9\times4 = 36^{\circ}$.

Answer:

$x = 4$; $m\angle HEB=36^{\circ}$