Question

Two parallel lines are crossed by a transversal. Parallel lines x and y are cut by transversal w. On line x where it intersects with line w, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 2, 4, 3, 1. On line y where it intersects with line w, 4 angles are created. Labeled clockwise, from uppercase left, the angles are: 6, 8, 7, 5. If mAngle6 = 123.5°, then mAngle1 is

Answer 1

Answer: The size of angle 1 is 56.5°

Step-by-step explanation: Please refer to the diagram attached.

The question gives us two parallel lines x and y as shown in the attachment. Then both parallel lines are cut by a transversal line w.

The transversal eventually results in four angle being formed at each point of intersection, both in line x and in line y. In line x, the angles formed are given as angles, 2, 4, 3 and 1. In line y, the angles formed are 6, 8, 7 and 5.

It is important to note that with the inclusion of the transversal line w, there is a relationship between the angles. looking at line y, we have one of the angles measuring 123.5 degrees (angle 6). That means angle 8 is derived as follows;

Angle 8 + Angle 6 = 180 (Angles on a straight line equals 180)

Angle 8 + 123.5 = 180

Subtract 123.5 from both sides of the equation

Angle 8 = 56.5 degrees

Note also that angle 5 is opposite angle 8 and opposite angles are equal. Therefore angle 5 equals 56.5 degrees as well.

Looking at line x, angle 1 is alternate to angle 8 (alternate interior angles are equal), therefore angle 1 equals 56.5 degrees also.

The diagram and the accompanying explanation shows that angle 1 measures 56.5°

Answer 2

Answer:

Corresponding angles theorem

linear pair postulate

definition of supplementary angles

Step-by-step explanation:

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