Complete the proof that m∠SVU + m∠RSV = 180°.
Understand the Problem
The question is asking to complete a geometric proof that shows the sum of the measures of angles SVU and RSV is equal to 180 degrees based on given angles and relationships from parallel lines cut by a transversal.
Answer
The proof confirms that $m\angle SVU + m\angle RSV = 180^\circ$.
Answer for screen readers
The proof shows that $m\angle SVU + m\angle RSV = 180^\circ$.
Steps to Solve
- Identify Given Information
The problem states that $RT \parallel UW$. This means that line $RT$ is parallel to line $UW$.
- Use Corresponding Angles Theorem
Since $RT \parallel UW$ and $XS$ is a transversal, we can use the Corresponding Angles Theorem. This means that $$ \angle SVU = \angle QSR $$ is true because they are corresponding angles.
- Substitute Corresponding Angles
Now we can write the equation for the sum of the angles: $$ m\angle QSR + m\angle RSV = 180^\circ $$ This is because angles on a straight line add up to $180^\circ$.
- Use Substitution to Complete Proof
Next, replace $m\angle QSR$ with $m\angle SVU$ since they are equal: $$ m\angle SVU + m\angle RSV = 180^\circ $$ This completes the proof that $m\angle SVU + m\angle RSV = 180^\circ$.
The proof shows that $m\angle SVU + m\angle RSV = 180^\circ$.
More Information
This result stems from properties of parallel lines cut by a transversal, where corresponding angles are equal, and angles that are adjacent along a straight line sum to $180^\circ$.
Tips
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Incorrectly Assuming Angles Are Not Corresponding: Ensure to correctly identify corresponding angles when parallel lines are involved.
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Forgetting the Supplementary Angle Property: Many forget that angles on a straight line must sum to $180^\circ$. Always check this property.
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