The relationships between angles 1, a, b, and 2 can be defined using the angles between parallel lines.
In the diagram, we can see the fences, making angles 1 and 2 with the parallel lines X and Y respectively.
Using the angles among parallel lines, we can state the relationships between angles 1, a, b, and 2 as follows:
- Angle 1 and Angle a are adjacent angles, thus their sum is 180°, that is m∠ 1 + m∠ a = 180°.
- Angle 2 and Angle b are adjacent angles, thus their sum is 180°, that is m∠ 2 + m∠ b = 180°.
- Angle 1 and Angle b are corresponding angles, thus they are equal, that is m∠1 = m∠ b.
- Angle 2 and Angle a are corresponding angles, thus they are equal, that is m∠2 = m∠ a
- Angle 1 and angle 2 are co-exterior angles, thus their sum is 180°, that is, m∠ 1 + m∠ 2 = 180°.
- Angle a and angle b are co-interior angles, thus their sum is 180°, that is, m∠ a + m∠ b = 180°.
These were the relations among angles 1, a, b, and 2, using the parallel lines X and Y.
Refer to the diagram for a better understanding.
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