Answer :
Step-by-step explanation:
Given that \(AOB\) is a straight line, we know that the angles formed along a straight line sum up to \(180^\circ\).
Let's denote the angles as follows:
- Angle \(AOC = 4x - 25\)
- Angle \(COB = x - 10\)
- Angle \(BOA = x + 5\)
Since \(AOB\) is a straight line, we have:
\[
AOC + COB + BOA = 180^\circ
\]
Substituting the given expressions for the angles:
\[
(4x - 25) + (x - 10) + (x + 5) = 180
\]
Combine like terms:
\[
4x + x + x - 25 - 10 + 5 = 180
\]
\[
6x - 30 = 180
\]
Add 30 to both sides to isolate the term with \(x\):
\[
6x = 210
\]
Divide both sides by 6:
\[
x = 35
\]
Therefore, the value of \(x\) is \(35\).
