Question

Z1 and Z2 are a linear pair. mZ1 = x-32, and mZ2 = x+82. Find the measure of each

angle.
A) Z1 = 33, 22 - 147
B) Z1 - 65, 22 - 115
C) Z1 = 33, Z2 = 157
D) Z1 = 65, Z2 = 125

Answer 1

After setting up an equation to find the value of x for the measures of angles Z1 and Z2 that form a linear pair, we find x equals 65, which gives us the measures Z1 = 33 degrees and Z2 = 147 degrees.

Step-by-step explanation:

Since Z1 and Z2 form a linear pair, they are adjacent angles whose measures add up to 180 degrees. We have mZ1 = x - 32, mZ2 = x + 82, and mZ1 + mZ2 = 180 degrees. To find the value of x, we set up the equation: (x - 32) + (x + 82) = 180.

Combining like terms, we get:

• 2x + 50 = 180
• 2x = 130
• x = 65

Now we can substitute x back into the expressions for mZ1 and mZ2:

• mZ1 = 65 - 32 = 33 degrees
• mZ2 = 65 + 82 = 147 degrees

Therefore, the measures of each angle are:

• Z1 = 33 degrees
• Z2 = 147 degrees