Question

if \\( \overrightarrow { o g } - \overrightarrow { o h } - \overrightarrow { o i } \\), and if \\( m \angle g o h = 6 x - 2 \\), \\( m \angle g o i = 8 x + 1 \\), and \\( m \angle h o i = 17 \\), then find \\( m \angle g o i \\).
after you enter your answer press go.
\\( m \angle g o i = \\)

Explanation:

Step1: Use angle - addition postulate

Since \(OG - OH - OI\), by the angle - addition postulate, \(m\angle GOI=m\angle GOH + m\angle HOI\).
Substitute the given expressions: \(8x + 1=(6x - 2)+17\).

Step2: Solve the equation for \(x\)

Simplify the right - hand side of the equation: \(8x + 1=6x+15\).
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 \(2\): \(x = 7\).

Step3: Find \(m\angle GOI\)

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

Answer:

\(57\)