Sure! Let’s solve this step by step.
Given:
- Angle 1 measures [tex]\((4x + 28)^\circ\)[/tex]
- The angle adjacent to the alternate exterior angle with angle 1 measures [tex]\((14x + 8)^\circ\)[/tex]
Two adjacent angles on a straight line add up to [tex]\(180^\circ\)[/tex] because they are supplementary.
Thus, we can set up the following equation based on the given angles being supplementary:
[tex]\[ (4x + 28) + (14x + 8) = 180 \][/tex]
Now, let's solve the equation step-by-step:
1. Combine like terms:
[tex]\[ 4x + 14x + 28 + 8 = 180 \][/tex]
[tex]\[ 18x + 36 = 180 \][/tex]
2. Subtract 36 from both sides of the equation:
[tex]\[ 18x = 180 - 36 \][/tex]
[tex]\[ 18x = 144 \][/tex]
3. Divide both sides by 18 to solve for [tex]\(x\)[/tex]:
[tex]\[ x = \frac{144}{18} \][/tex]
[tex]\[ x = 8 \][/tex]
So, the value of [tex]\(x\)[/tex] is [tex]\( \boxed{8} \)[/tex].
