To solve for [tex]\( x \)[/tex] given the conditions regarding angles 1 and 3, let's break the problem down step by step.
1. Understand the given information:
- The measure of angle 1 is [tex]\( 110^\circ \)[/tex].
- The measure of angle 3 is [tex]\( (2x + 10)^\circ \)[/tex].
- Angle 1 and angle 3 form a linear pair, meaning they are supplementary.
2. Recall the property of supplementary angles:
- Supplementary angles are two angles that add up to [tex]\( 180^\circ \)[/tex].
3. Set up the equation using the fact that the angles are supplementary:
- Since angle 1 and angle 3 are supplementary, their measures add up to [tex]\( 180^\circ \)[/tex].
- This can be written as:
[tex]\[
110^\circ + (2x + 10)^\circ = 180^\circ
\][/tex]
4. Combine like terms and solve for [tex]\( x \)[/tex]:
- First, simplify the equation:
[tex]\[
110 + 2x + 10 = 180
\][/tex]
- Combine the constant terms on the left-hand side:
[tex]\[
120 + 2x = 180
\][/tex]
- Subtract 120 from both sides to isolate the term with [tex]\( x \)[/tex]:
[tex]\[
2x = 60
\][/tex]
- Finally, divide both sides by 2 to solve for [tex]\( x \)[/tex]:
[tex]\[
x = 30
\][/tex]
5. Conclusion:
- The value of [tex]\( x \)[/tex] is [tex]\( 30 \)[/tex].
Therefore, [tex]\( x \)[/tex] equals [tex]\( 30 \)[/tex].
