When two lines are parallel the angles made by a third line crossing them have certain properties.
Corresponding angles
Corresponding angles on parallel lines are equal.
The following diagram shows the four possible pairs of corresponding angles.
Alternate angles
Alternate angles on parallel lines are equal.
The following diagram shows the two possible pairs of alternate angles.
Co-interior angles
Co-interior angles on parallel lines are add up to 180o (supplementary angles).
The following diagram shows the two possible pairs of co-interior angles.
Using these angle properties, the size of angles on parallel lines can be found.
Examples
Example One
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Example Two
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Example Three
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x = 105o
Reason: Corresponding angles on parallel lines are equal.
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y = 65o
Reason: Alternate angles on parallel lines are equal.
z + y = 180 z + 65 = 180 z = 115o
Reason: Angles on a staraight line add up to 180 degrees.
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w + 75 = 180 w = 105o
Reason: Co-interior angles on parallel lines add up to 180o
t = 105o
Reason: Vertically opposite angles are equal.
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