Question

problem 19: (first taught in lesson 10) if $overrightarrow{ef}-overrightarrow{eg}-overrightarrow{eh}$ and if $mangle feg = 17x + 1$, $mangle geh = 23$, and $mangle feh = 22x + 4$, then find $mangle feh$. after you enter your answer press go. $mangle feh = $

Explanation:

Step1: Use angle - addition postulate

Since $\angle FEH=\angle FEG+\angle GEH$, we have the equation $22x + 4=(17x + 1)+23$.

Step2: Simplify the right - hand side

$(17x + 1)+23=17x+24$. So the equation becomes $22x + 4=17x+24$.

Step3: Solve for x

Subtract $17x$ from both sides: $22x-17x + 4=17x-17x+24$, which simplifies to $5x+4 = 24$. Then subtract 4 from both sides: $5x+4 - 4=24 - 4$, getting $5x=20$. Divide both sides by 5: $x = 4$.

Step4: Find m∠FEH

Substitute $x = 4$ into the expression for $\angle FEH$. $m\angle FEH=22x + 4=22\times4+4=88 + 4=92$.

Answer:

$92$