Final Answer:
The measure of angle ∠IMN is 83 degrees.
Step-by-step explanation:
In the given scenario, we have two angles whose measures are related, and we are required to find the value of 'm∠IMN'.
Let's denote the measure of 'm∠LMI' as '7x + 13'. According to the problem, 'm∠LMN' = 158°, and 'm∠IMN' = '6x + 2'.
Since 'm∠LMI' + 'm∠IMN' = 'm∠LMN' in a triangle, we can set up the equation:
(7x + 13) + (6x + 2) = 158.
Combine like terms:
13x + 15 = 158.
Subtract 15 from both sides:
13x = 143.
Divide by 13:
x = 11.
Now that we have the value for 'x', we can substitute it back into 'm∠IMN = 6x + 2':
m∠IMN = 6(11) + 2 = 68 + 2 = 70.
Therefore, 'm∠IMN' is 70 degrees.