Question

1. in the diagram, $overline{ab}$ and $overline{ce}$ are perpendicular. if $mangle ceh=(6x)^{circ}$ and $mangle heb=(8x + 6)^{circ}$, what is the value of $x$ and the $mangle ceh$?

Explanation:

Step1: Use perpendicular - angle property

Since $\overline{AB}$ and $\overline{CE}$ are perpendicular, $\angle CEB = 90^{\circ}$. And $\angle CEB=\angle CEH+\angle HEB$, so $6x+(8x + 6)=90$.

Step2: Simplify the equation

Combine like - terms: $6x+8x+6 = 90$, which gives $14x+6 = 90$.

Step3: Solve for $x$

Subtract 6 from both sides: $14x=90 - 6=84$. Then divide both sides by 14, so $x=\frac{84}{14}=6$.

Step4: Find the measure of $\angle CEH$

Substitute $x = 6$ into the expression for $\angle CEH$. $m\angle CEH=6x$, so $m\angle CEH=6\times6 = 36^{\circ}$.

Answer:

$x = 6$, $m\angle CEH=36^{\circ}$