a is parallel to b.
Calculate the angles shown in the diagram.
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a is parallel to b.
Calculate the angles shown in the diagram.
Given that according to the definition, the vertex angles are equal to each other, it can be argued that:
Now we can calculate the second pair of vertex angles in the same circle:
Since the sum of a plane angle is 180 degrees, angle 1 and angle 3 are complementary to 180 degrees and equal to 65 degrees.
We now notice that between the parallel lines there are corresponding and equal angles, and they are:
Since angle 4 is opposite to angle 6, it is equal to it and also equal to 65 degrees.
Another pair of alternate angles are angle 1 and angle 5.
We have proven that:
Therefore, angle 5 is also equal to 65 degrees.
Since angle 7 is opposite to angle 5, it is equal to it and also equal to 115 degrees.
That is:
1, 3 , 5, 7 = 65°; 2, 4 , 6 = 115°
If one of two corresponding angles is a right angle, then the other angle will also be a right angle.
Corresponding angles are in the same relative position at each intersection. If one angle is at the top-right of the first intersection, its corresponding angle is at the top-right of the second intersection.
Adjacent angles on a straight line are supplementary - they add to 180°. So if one angle is 115°, the angle next to it must be .
Vertical angles are opposite each other at the same intersection point and are always equal. Corresponding angles are at different intersection points but in the same relative positions.
Focus on understanding the patterns rather than memorizing names. Remember: opposite angles are equal, adjacent angles sum to 180°, and parallel lines create matching angles.
Verify that: (1) All angles around each intersection point sum to 360°, (2) Adjacent angles sum to 180°, and (3) Corresponding angles are equal between the parallel lines.
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