To solve for [tex]\( x \)[/tex] given the angles [tex]\( 155^\circ, 140^\circ, 95^\circ, 125^\circ, 115^\circ, (x+10)^\circ \)[/tex], let's follow these steps:
1. Calculate the sum of the given angles (excluding [tex]\( x \)[/tex]):
Sum of the given angles = [tex]\( 155^\circ + 140^\circ + 95^\circ + 125^\circ + 115^\circ = 630^\circ \)[/tex].
2. Identify the total sum of angles in the figure:
Since the exact nature of the figure is not specified, let's consider a commonly used total angle sum of [tex]\( 360^\circ \)[/tex] (typically a full circle or a part of some specific polygon's internal angle sum). Note that the total angle sum may vary based on the shape of the polygon (e.g., for a pentagon, the internal angle sum is 540 degrees).
3. Calculate the angle sum including [tex]\( (x + 10)\)[/tex]:
Total angle sum = 360 degrees.
Therefore, we use the equation:
[tex]\[
630^\circ + (x + 10)^\circ = 360^\circ
\][/tex]
4. Solve for [tex]\( x \)[/tex]:
[tex]\[
630^\circ + (x + 10)^\circ = 360^\circ
\][/tex]
Simplify to isolate [tex]\( x \)[/tex]:
[tex]\[
(x + 10)^\circ = 360^\circ - 630^\circ
\][/tex]
[tex]\[
(x + 10)^\circ = -270^\circ
\][/tex]
Now, subtract 10 from both sides:
[tex]\[
x = -270^\circ - 10^\circ
\][/tex]
[tex]\[
x = -280^\circ
\][/tex]
Therefore, the values are:
- Given angles sum: [tex]\( 630^\circ \)[/tex]
- Total angle sum assumed: [tex]\( 360^\circ \)[/tex]
- Sum including [tex]\( (x + 10)^\circ \)[/tex]: [tex]\( -270^\circ \)[/tex] after equating to total angle sum
- Value of [tex]\( x \)[/tex]: [tex]\( -280^\circ \)[/tex]
Since the calculated value of [tex]\( x \)[/tex] is not among the provided coloring options, it seems [tex]\( x = -280^\circ \)[/tex] does not apply for either [tex]\( x=65^\circ \)[/tex] or [tex]\( x=130^\circ \)[/tex]. This suggests a discrepancy based on the assumed total angle sum or the angle configuration in the problem. Further clarification on the geometry specifics would be required to resolve this within the context of accurate figure properties.
