Final answer:
Two angles form a linear pair when their sum is 180 degrees. By setting up and solving equations based on the given information, we can find the measures of both angles.
Step-by-step explanation:
A linear pair of angles is formed when two angles are adjacent and their sum is 180 degrees. Let's denote the measure of angle 1 as x and angle 2 as y.
According to the given information, x is eight more than y, so we can write the equation: x = y + 8.
Since ∠1 and ∠2 form a linear pair, their sum is 180 degrees, so we can write another equation: x + y = 180.
Now, we can solve the system of equations to find the measures of both angles.
Substituting the value of x from the first equation into the second equation, we have (y + 8) + y = 180.
Simplifying this equation gives us 2y + 8 = 180. Subtracting 8 from both sides gives 2y = 172.
Finally, dividing both sides by 2 gives y = 86.
Substituting this value back into any of the equations, we can find the value of x. Using the first equation x = y + 8, we have x = 86 + 8 = 94.
Therefore, ∠1 measures 94 degrees and ∠2 measures 86 degrees.