angle 1 and angle 2 are a linear pair. mangle 1 = x – 30, and mangle 2 = x + 76. Find the measure of each angle.

Answer 1

A linear pair of angles are two adjacent angles whose sum adds up to 180 degrees.

Let's set up an equation to solve for x:

(x-30) + (x+76) = 180

Combining like terms:

2x + 46 = 180

Subtracting 46 from both sides:

2x = 134

Dividing both sides by 2:

x = 67

Now we can substitute x back into the given expressions to find the measure of each angle:

mangle 1 = x - 30

mangle 1 = 67 - 30

mangle 1 = 37

mangle 2 = x + 76

mangle 2 = 67 + 76

mangle 2 = 143

Therefore, angle 1 measures 37 degrees and angle 2 measures 143 degrees.