Find the values of a, b, and c if lines m and n are parallel. Note: This diagram is not to scale.
Parallel lines are cut by three transversals. Some angles that are formed are labeled with their angle measures while some others are labeled as a, b, and c.Horizontal, parallel lines m and n are shown. Three transversals cut through the parallel lines, intersecting line m in three different points but intersecting line n all at the same point. Several angles between the two parallel lines are labeled. The first transversal on the far left intersects line m and then slopes down and to the right in order to intersect with line n. Where it crosses line m, the angle in the bottom right corner is labeled as a degrees. Where it crosses line n the angle in the top left corner is labeled 36 degrees. The second transversal is to the right of the first but also intersects line m and then slopes down and to the right in order to intersect with line n. Where it crosses line m, the angle on the bottom left is labeled as b degrees and the angle on the bottom right is labeled as c degrees. The third transversal on the far right intersects line m and then slopes down and to the left in order to intersect with line n. Where it crosses line m the angle on the bottom right is labeled 139 degrees. The angle formed above line n in between the second and third transversals is labeled 77 degrees.
(1 point)
Responses
a = 41, b = 144, c = 36
a = 41, b = 144, c = 36
a = 77, b = 118, c = 62
a = 77, b = 118, c = 62
a = 36, b = 103, c = 77
a = 36, b = 103, c = 77
a = 36, b = 118, c = 62
a = 36, b = 118, c = 62
To find the values of a, b, and c, we can use the properties of parallel lines and their corresponding angles.
Since line n is parallel to line m, the angle labeled 36 degrees and the angle labeled a degrees are corresponding angles. Therefore, a = 36 degrees.
Similarly, the angle labeled 77 degrees and the angle labeled c degrees are also corresponding angles. Therefore, c = 77 degrees.
Now, let's focus on finding the value of b.
Since line n is parallel to line m, the angle labeled 77 degrees and the angle labeled b degrees are alternate interior angles. Therefore, b = 77 degrees.
Therefore, the values of a, b, and c are:
a = 36 degrees
b = 77 degrees
c = 77 degrees
To find the values of a, b, and c, we need to use the properties of parallel lines and transversals.
First, let's focus on the angles labeled on the diagram. We are given that the angle formed above line n between the second and third transversals is labeled 77 degrees. This angle is formed by the line n and the second transversal. Since line m and line n are parallel, the angle formed by line m and the second transversal will also be 77 degrees.
Next, we can look at the angles formed by the first transversal. We know that the angle formed by line m and the first transversal is labeled as a degrees, and the angle formed by line n and the first transversal is labeled as 36 degrees. Again, since line m and line n are parallel, the angles formed by the second and third transversals will also be a degrees and 36 degrees, respectively.
Now, let's focus on the angles formed by the second and third transversals. We are given that the angle formed by line m and the third transversal is labeled as 139 degrees. Since the angle formed by line n and the second transversal (which is also 77 degrees) are corresponding angles, the angle formed by line m and the second transversal will also be 139 degrees.
Using these angles, we can solve for the values of a, b, and c:
From the information given:
a = 36 degrees (angle formed by first transversal and line m)
b = 77 degrees (angle formed by second transversal and line m)
c = 139 degrees (angle formed by third transversal and line m)
Therefore, the values of a, b, and c are:
a = 36 degrees, b = 77 degrees, c = 139 degrees.