Question

find x
if $overline{cd}perpoverline{ef}$, $mangle ech=(x + 5)^{circ}$ and $mangle hcd=(3x - 7)^{circ}$, find each missing value.

Explanation:

Step1: Use perpendicular - angle property

Since $\overline{CD}\perp\overline{EF}$, $\angle ECD = 90^{\circ}$, and $\angle ECH+\angle HCD=\angle ECD = 90^{\circ}$.
So, $(x + 5)+(3x-7)=90$.

Step2: Simplify the left - hand side of the equation

Combine like terms: $x+3x + 5-7=90$, which simplifies to $4x-2 = 90$.

Step3: Isolate the variable term

Add 2 to both sides of the equation: $4x-2 + 2=90 + 2$, getting $4x=92$.

Step4: Solve for x

Divide both sides by 4: $x=\frac{92}{4}=23$.

Answer:

$x = 23$