Find the measure of each angle of the supplementary angles, given the measure of angle 1 = (-10x + 53) and the measure of angle 2 = (-5x - 8).
Supplementary means adds up to 180. Complementary adds up to 90. -10x+53-5x-8=180
which equation can be used to find the measure of angle GFE?
To find the measures of the supplementary angles, we need to know their sum. Supplementary angles add up to 180 degrees.
So, we can set up an equation:
(angle 1) + (angle 2) = 180
Substituting the given measures of angle 1 and angle 2, we have:
(-10x + 53) + (-5x - 8) = 180
To solve this equation, let's simplify and combine like terms:
-10x + 53 - 5x - 8 = 180
-15x + 45 = 180
Next, we can isolate the variable on one side of the equation by subtracting 45 from both sides:
-15x = 180 - 45
-15x = 135
Now, divide both sides of the equation by -15 to solve for x:
x = 135 / -15
x = -9
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 measures.
For angle 1:
angle 1 = (-10x + 53) = (-10(-9) + 53) = 143 degrees
For angle 2:
angle 2 = (-5x - 8) = (-5(-9) - 8) = 37 degrees
Therefore, angle 1 measures 143 degrees, and angle 2 measures 37 degrees.