Final answer:
To find the measures of angles ∠1 and ∠2 that form a linear pair, set up and solve the equation (5x + 9) + (3x + 11) = 180. After finding x = 20, substitute it back into the expressions to get m∠1 = 109° and m∠2 = 71°.
Step-by-step explanation:
The question involves finding the measures of two angles, ∠1 and ∠2, that form a linear pair. This means that their measures add up to 180 degrees since they are adjacent and their non-common sides form a straight line. We are given m∠1 as (5x + 9)° and m∠2 as (3x + 11)°. To find the measures, we set up an equation: (5x + 9) + (3x + 11) = 180. Solving for x, we get:
- 8x + 20 = 180
- 8x = 160
- x = 20
Having found x, we then substitute it back into the original expressions for m∠1 and m∠2:
- m∠1 = (5x + 9)° = (5(20) + 9)° = 109°
- m∠2 = (3x + 11)° = (3(20) + 11)° = 71°
Therefore, the measures of angles ∠1 and ∠2 are 109° and 71°, respectively.