Use the image to answer the question. a. Write an equation for these two supplementary angles. (1 point) b. Explain how to solve for the value of x. (1 point) c. Find the measurement of each angle. Make sure to list both. (2 points) (4 points)
a. The equation for the two supplementary angles can be written as:
angle1 + angle2 = 180 degrees
b. To solve for the value of x, we can set up the equation based on the given information. We know that angle1 + angle2 = 180 degrees. From the diagram, we can see that angle1 is labeled as 2x - 20 degrees and angle2 is labeled as 3x + 10 degrees. We can substitute these values into the equation:
(2x - 20) + (3x + 10) = 180
Now, we can solve for x.
c. Let's solve the equation from part b:
5x - 10 = 180
Adding 10 to both sides:
5x = 190
Dividing both sides by 5:
x = 38
Now that we have the value of x, we can substitute it back into the given expressions for angle1 and angle2 to find their measurements:
Angle1 = 2x - 20 = 2(38) - 20 = 76 - 20 = 56 degrees
Angle2 = 3x + 10 = 3(38) + 10 = 114 + 10 = 124 degrees
Therefore, angle1 measures 56 degrees and angle2 measures 124 degrees.