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QuestionMathematics

Do corresponding angles sum up to 180 degrees?
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Step 1:
I'll solve this problem step by step:

Step 2:
: Understanding Corresponding Angles

Corresponding angles are formed when a transversal crosses two parallel lines. These angles have specific geometric properties that we'll explore.

Step 3:
: Definition of Corresponding Angles

Corresponding angles are located in the same relative position when a transversal crosses two lines. When the lines are parallel, corresponding angles have a special relationship.

Step 4:
: Key Property of Corresponding Angles

Corresponding angles are always congruent (equal in measure) when the lines are parallel.

Step 5:
: Angle Sum Verification

- If the lines are parallel, corresponding angles will always have the same measure. - However, they do NOT necessarily sum to 180 degrees. - Each corresponding angle will be equal to its counterpart, but this doesn't mean their sum is 180 degrees.

Step 6:
: Counterexample

- Their sum would be $$60° + 60° = 120°$$, not 180 degrees
Consider two parallel lines cut by a transversal: - If one corresponding angle is 60 degrees - Its corresponding angle will also be 60 degrees

Final Answer

When lines are parallel, corresponding angles are equal, but their sum depends on the specific angle measurements of the transversal.