Question

problem 15: if $overrightarrow{og}-overrightarrow{oh}-overrightarrow{oi}$, and if $mangle goh = 6x - 2$, $mangle goi = 8x + 1$, and $mangle hoi = 17$, then find $mangle goi$. after you enter your answer press go. $mangle goi =$

Explanation:

Step1: Use angle - addition postulate

Since $\overrightarrow{OG}-\overrightarrow{OH}-\overrightarrow{OI}$, we have $m\angle GOI=m\angle GOH + m\angle HOI$.
So, $8x + 1=(6x - 2)+17$.

Step2: Solve the equation for x

First, simplify the right - hand side of the equation: $(6x - 2)+17=6x+15$.
The equation becomes $8x + 1=6x + 15$.
Subtract $6x$ from both sides: $8x-6x + 1=6x-6x + 15$, which gives $2x+1 = 15$.
Subtract 1 from both sides: $2x+1 - 1=15 - 1$, so $2x=14$.
Divide both sides by 2: $\frac{2x}{2}=\frac{14}{2}$, and $x = 7$.

Step3: Find $m\angle GOI$

Substitute $x = 7$ into the expression for $m\angle GOI$: $m\angle GOI=8x + 1$.
$m\angle GOI=8\times7+1=56 + 1=57$.

Answer:

57