Final answer:
The measure of angle Z1 is 41.5°, and the measure of angle 2 is 138.5°, found by solving the linear pair equation set up by their angle expressions mZ1 = (5x + 9)° and m2 = (3x + 119)° which must sum to 180°.
Step-by-step explanation:
When angles form a linear pair, they are adjacent and their non-common sides form a straight line. This means that the two angles add up to 180 degrees. From the given information, we have two expressions for the angles: mZ1 = (5x + 9)° and m2 = (3x + 119)°. To find the measure of each angle, we set up the equation:
5x + 9 + 3x + 119 = 180
Combining like terms, we get:
8x + 128 = 180
Subtracting 128 from both sides gives us:
8x = 52
Dividing by 8, we find:
x = 6.5
Now, we plug this value back into the original expressions to find each angle:
mZ1 = 5(6.5) + 9 = 32.5 + 9 = 41.5°
m2 = 3(6.5) + 119 = 19.5 + 119 = 138.5°
Therefore, the measure of angle Z1 is 41.5° and the measure of angle 2 is 138.5°.