angle 1 and angle 2 are a linear pair. mangle 1 = x – 30, and mangle 2 = x + 76. Find the measure of each angle.
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.
To find the measure of each angle, we can set up an equation using the fact that angles 1 and 2 are a linear pair.
A linear pair of angles is formed when two angles are adjacent (share a common vertex and side) and their non-common sides form a straight line.
Given that angle 1 has a measure of x – 30 and angle 2 has a measure of x + 76, we can set up the equation:
(x – 30) + (x + 76) = 180
Simplifying the equation:
2x + 46 = 180
Next, we can solve for x by isolating it on one side of the equation:
2x = 180 – 46
2x = 134
Dividing both sides of the equation by 2:
x = 134 / 2
x = 67
Now that we have found the value of x, we can substitute it back into the expressions for angle 1 and angle 2 to find their respective measures:
Angle 1: x – 30 = 67 – 30 = 37 degrees
Angle 2: x + 76 = 67 + 76 = 143 degrees
Therefore, angle 1 measures 37 degrees and angle 2 measures 143 degrees.
To find the measure of each angle, we can use the fact that angles in a linear pair add up to 180 degrees.
Let's set up an equation using the given information:
m(angle 1) + m(angle 2) = 180
Substituting the given values:
(x - 30) + (x + 76) = 180
Now, solve this equation to find the value of x:
2x + 46 = 180
Subtract 46 from both sides:
2x = 134
Divide both sides by 2:
x = 67
Now that we have the value of x, we can substitute it back into the expressions for the angles to find their measures:
m(angle 1) = x - 30 = 67 - 30 = 37 degrees
m(angle 2) = x + 76 = 67 + 76 = 143 degrees
Therefore, the measure of angle 1 is 37 degrees and the measure of angle 2 is 143 degrees.