Identify each pair of angles as corresponding, alternate interior, alternate exterior, or consecutive interior. Find the measure of each angle indicated.
Understand the Problem
The question involves identifying angles formed by parallel lines and a transversal, and requires finding the measures of various indicated angles based on the relationships between them.
Answer
11) $68^\circ$; 12) $100^\circ$; 13) $80^\circ$; 14) $67^\circ$; 15) $127^\circ$; 16) $83^\circ$; 17) $57^\circ$; 18) $113^\circ$
Answer for screen readers
- $68^\circ$
- $100^\circ$
- $80^\circ$
- $67^\circ$
- $127^\circ$
- $83^\circ$
- $57^\circ$
- $113^\circ$
Steps to Solve
- Identify Angles Related to Parallel Lines and a Transversal
For each pair of parallel lines intersected by a transversal, recognize the relationships among the angles formed, such as corresponding angles, alternate interior angles, and consecutive interior angles.
- Apply Angle Relationships
Use the relationships to determine the measures of the unknown angles. For instance:
- Corresponding angles are equal.
- Alternate interior angles are equal.
- Consecutive interior angles are supplementary (they add up to $180^\circ$).
- Solve for Each Angle
For each specific question (11 to 18 in the document), list the given angle measures and apply the angle relationships to find the unknown angles.
- Example Calculation
For example, if the measure of angle is $x^\circ$ and it has corresponding angles equal to it, you can set them equal: $$ x = 112 $$
If working with consecutive interior angles, set up the equation: $$ x + 112 = 180 $$
- Conclusion
Present the measures of the angles you calculated, ensuring to label which angle corresponds to which measurement.
- $68^\circ$
- $100^\circ$
- $80^\circ$
- $67^\circ$
- $127^\circ$
- $83^\circ$
- $57^\circ$
- $113^\circ$
More Information
These angle measures are derived using properties of parallel lines cut by a transversal, which dictate the relationships between angles formed. Understanding these concepts is crucial in geometry.
Tips
- Confusing corresponding angles with alternate interior angles.
- Forgetting that consecutive interior angles are supplementary.
- Miscalculating angles by not correctly using the angle relationships.
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