Question

in the diagram, ab and ec are perpendicular. if m∠heb=(9x)° and m∠ceh=(13x + 2)°, then the value of x is 4 and m∠heb= select choice. 27 36 54

Explanation:

Step1: Recall perpendicular - angle property

Since $\overrightarrow{AB}$ and $\overrightarrow{EC}$ are perpendicular, $\angle BEC = 90^{\circ}$. And $\angle BEC=\angle HEB+\angle CEH$.

Step2: Set up the equation

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

Step3: Combine like - terms

Combining the $x$ terms, we get $(9x+13x)+2 = 90$, 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 $\angle HEB$

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

Answer:

$x = 4$; $m\angle HEB=36$