Angle Pair Relationships Created by a Transversal and 2 parallel lines
Consecutive Exterior Angles
Definition: Angles that are on the same side of the transversal, but outside the parallel lines
If one angle is acute, the other angle must be obtuse.
One consecutive exterior angle could be 50 degrees, the other angle would have to be 130 degrees.
The sum of the consecutive exterior angle pair is 180 degrees.
Alternate Exterior Angles
Definition: Angles that are on opposite sides of the transversal, but on the outside of the parallel lines
Alternate Interior angles are congruent.
If one angle is 153 degrees, its alternate exterior angle pair would also be 153 degrees.
If one angle is (3x+15) degrees and the other angle pair is 75 degrees. You can find the value of x and the missing value using the equation:
3x + 15 = 75
3x + 15 = 75
3x = 60
x = 20
Both angles equal 75 degrees.
3(20)+15 = 75
Corresponding Angles
Corresponding angles are congruent.
If one angle is 30 degrees, its corresponding angle pair would also be 30 degrees
If one angle is (2x-5) degrees and the other angle is 105 degrees. You can find the value of x and the missing value using the equation:
2x - 5 = 105
2x - 5 = 105
2x = 110
x = 55
Both angles equal 105 degrees.
2(55)-5 = 105
Both angles will be acute or both angles will be obtuse.
Definition: Angles that are on the same spot, but on a different line
Consecutive Interior Angles
Consecutive interior angles are supplementary--they add to 180 degrees
Definition: Angles that are on the same side of the transversal but inside the parallel lines
If one angle is (2x-5) degrees and the other angle is 105 degrees. You can find the value of x and the missing value using the equation:
2x - 5 + 105 = 180
2x + 110 = 180
2x = 70
x = 35
One angle was given (150 degrees), the other angle is 30.
If one angle is acute, the other angle must be obtuse.
Alternate Interior Angles
Alternate Interior angles are congruent.
If one angle is 45 degrees, its alternate interior angle pair would also be 45 degrees.
Definition: Angles that are on opposite sides of the transversal, but inside the parallel lines
2 alternate interior angle pairs are created when parallel lines are cut by a transversal.
