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°
