a. Write an equation for these two supplementary angles.
b. Explain how to solve for the value of x.
c. Find the measurement of each angle. Make sure to list both.
Angles:
(2x + 3)
(x-6)
a. The equation for two supplementary angles is:
(2x + 3) + (x - 6) = 180
b. To solve for the value of x, we need to solve the equation (2x + 3) + (x - 6) = 180. This equation represents the sum of both angles being equal to 180 degrees, as supplementary angles always add up to 180 degrees.
To solve the equation, we can simplify it by combining like terms:
2x + 3 + x - 6 = 180
3x - 3 = 180
Next, we isolate the variable x by adding 3 to both sides of the equation:
3x - 3 + 3 = 180 + 3
3x = 183
Finally, we divide both sides of the equation by 3 to solve for x:
3x/3 = 183/3
x = 61
c. Now that we have found the value of x, we can substitute it back into the given expressions to find the measurement of each angle.
For the first angle: (2x + 3)
(2 * 61 + 3) = 122 + 3 = 125 degrees
For the second angle: (x - 6)
(61 - 6) = 55 degrees
Therefore, the measurement of the first angle is 125 degrees and the measurement of the second angle is 55 degrees.