Answer:
- m>d = 40 degrees
- m>a = 140 degrees
- m>c = 140 degrees
- m>x = 140 degrees
- m>z = 140 degrees
Step-by-step explanation:
If two parallel lines are cut by a transversal, the corresponding angles are congruent.
In this case, the angle measure of 40 degrees corresponds to the identical angle on the other straw, m>b. It also corresponds to angles directly opposite the transversal, such as m>y and m>d.
So:
- m>b = 40 degrees
- m>y = 40 degrees
- m>d = 40 degrees
To have complete angle measurements, the total angles need to add to 360 degrees. As such:
[tex]x + y + z + 40 = 360[/tex], and
[tex]a + b + c + d = 360[/tex]
knowing y = 40, we can solve for x and z by simplifying the equation to
[tex]x + z = 280[/tex]
Because the angles are congruent because of the parallel lines, both angles are 140 and add to 280.
- m>d = 40 degrees
- m>a = 140 degrees
- m>c = 140 degrees
- m>x = 140 degrees
- m>z = 140 degrees
