In the figure below, angle y and angle x form vertical angles. Angle y forms a straight line with the 80° angle and the 60° angle.
A straight line is shown and is marked with three angles. The first angle measures 80 degrees. The second angle measures 60 degrees. The third angle is labeled y. The line between the 60 degree angle and angle y extends below the straight line. The angle formed is labeled angle x.
Write and solve an equation to determine the measure of angle x. (5 points)
Since angle y and angle x form vertical angles, they are congruent.
The sum of the measures of angles on a straight line is 180 degrees.
Therefore, we have:
x + y + 80 + 60 = 180
x + y + 140 = 180
x + y = 40
To solve for x, we need another equation. We know that angle y forms a straight line with the 80° angle and the 60° angle. So, the sum of their measures is 180 degrees.
Thus, we have:
80 + 60 + y = 180
140 + y = 180
y = 180 - 140
y = 40
Substituting the value of y into the equation x + y = 40, we get:
x + 40 = 40
x = 40 - 40
x = 0
Therefore, the measure of angle x is 0 degrees.
how would the angle x be 0 degrees.
I apologize for the mistake. You are correct, angle x cannot be 0 degrees.
Given that x + y = 40, and we know that y = 40, we can substitute y into the equation:
x + 40 = 40
Now, let's solve for x:
x = 40 - 40
x = 0
So, the measure of angle x is 0 degrees.
Why would it be 0 the degrees is supposed to be a number not 0
I apologize for the confusion caused by my previous response. You are correct, the measure of angle x cannot be 0 degrees if angle y is 40 degrees. Thank you for pointing out the error.
To calculate the measure of angle x, we can use the fact that angle y and angle x are vertical angles, which means they have the same measure.
Since angle y is given as 40 degrees, we can conclude that angle x is also 40 degrees. Thus, the measure of angle x is 40 degrees.