I'll solve each of these problems by applying the properties of alternate angles formed when two parallel lines are cut by a transversal.
Key Concepts:
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Alternate Interior Angles: When two parallel lines are cut by a transversal, alternate interior angles are equal.
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Alternate Exterior Angles: When two parallel lines are cut by a transversal, alternate exterior angles are equal.
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Corresponding Angles: When two parallel lines are cut by a transversal, corresponding angles are equal.
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Supplementary Angles: Angles that add up to 180° (often adjacent angles on a straight line).
Let me solve each problem one by one:
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Problem 1:
We have an angle of 144° and another of 36°. Since these are on a straight line, they should add up to 180° (144° + 36° = 180°). The angle marked 'x' is an alternate interior angle to the 36° angle. Therefore,
x = 36°.
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Problem 2:
We have angles of 131° and 49°. These are on a straight line (131° + 49° = 180°). The angle 'x' is an alternate interior angle to the 49° angle. Therefore,
x = 49°.
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Problem 3:
We have angles of 127° and 53°. These are on a straight line (127° + 53° = 180°). The angle 'x' is an alternate interior angle to the 53° angle. Therefore,
x = 53°.
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Problem 4:
We have angles of 62° and 118°. These are on a straight line (62° + 118° = 180°). The angle 'x' is an alternate interior angle to the 62° angle. Therefore,
x = 62°.
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Problem 5:
We have angles of 125° and 55°. These are on a straight line (125° + 55° = 180°). The angle 'x' is an alternate interior angle to the 55° angle. Therefore,
x = 55°.
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Problem 6:
We have angles of 102° and 78°. These are on a straight line (102° + 78° = 180°). The angle 'x' is an alternate interior angle to the 78° angle. Therefore,
x = 78°.
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Problem 7:
We have angles of 151° and 29°. These are on a straight line (151° + 29° = 180°). The angle 'x' is an alternate interior angle to the 29° angle. Therefore,
x = 29°.
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Problem 8:
We have angles of 83° and 97°. These are on a straight line (83° + 97° = 180°). The angle 'x' is an alternate interior angle to the 83° angle. Therefore,
x = 83°.
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Problem 9:
We have angles of 130° and 50°. These are on a straight line (130° + 50° = 180°). The angle 'x' is an alternate interior angle to the 50° angle. Therefore,
x = 50°.
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Final Answers:
1) x = 36°
2) x = 49°
3) x = 53°
4) x = 62°
5) x = 55°
6) x = 78°
7) x = 29°
8) x = 83°
9) x = 50°
Each solution uses the property that alternate interior angles are equal when two parallel lines are cut by a transversal.
Parent Tip: Review the logic above to help your child master the concept of parallel lines cut by a transversal worksheet 8th grade.
