Lines m and n are parallel, cut by a transversal. 1. Name the transversal. 2. Name a pair of alternate interior angles. 3. Name a pair of alternate exterior angles. 4. If m<1 = 125... Lines m and n are parallel, cut by a transversal. 1. Name the transversal. 2. Name a pair of alternate interior angles. 3. Name a pair of alternate exterior angles. 4. If m<1 = 125, what is m<2? How are they related to each other? 5. If m<4 = 84, what is m<7? How are they related to each other? 6. If m<6 = 110, find m<2. How are they related to each other? 7. If m<3 = 70, find m<8. How are they related to each other? 8. If m<5 = 120, find m<1. How are they related to each other? 9. If m<7 = 75, find m<8. How are they related to each other? 10. Interior angles on the same side of the transversal are NOT congruent. They are supplementary. a) How are interior angles related to each other? b) <3 and <6 are interior angles. If m<6 = 119, find m<3.
Understand the Problem
The image shows a set of geometry problems involving parallel lines cut by a transversal. The questions require identifying the transversal, naming pairs of angles (alternate interior, alternate exterior), and using angle relationships to find the measures of other angles, given the measure of one angle. Question 10 asks about the relationship between interior angles and the measure of angle 3 if angle 6 is 119 given that angle 3 and angle 6 are interior angles.
Answer
a) Interior angles on the same side of the transversal are supplementary. b) $m\angle3 = 61^\circ$
Answer for screen readers
a) Interior angles on the same side of the transversal are supplementary. b) $m\angle3 = 61^\circ$
Steps to Solve
- Understanding Supplementary Angles
Supplementary angles are two angles whose measures add up to 180 degrees.
- Applying the Supplementary Angle Relationship
Since angles 3 and 6 are interior angles on the same side of the transversal, they are supplementary according to the question. Therefore: $m\angle3 + m\angle6 = 180^\circ$
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Substituting the given value We are given that $m\angle6 = 119^\circ$. Substitute this value into the equation from step 2: $m\angle3 + 119^\circ = 180^\circ$
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Solving for $m\angle3$
Subtract $119^\circ$ from both sides of the equation: $m\angle3 = 180^\circ - 119^\circ$ $m\angle3 = 61^\circ$
a) Interior angles on the same side of the transversal are supplementary. b) $m\angle3 = 61^\circ$
More Information
When two parallel lines are intersected by a transversal, interior angles on the same side of the transversal are always supplementary, meaning their measures add up to 180 degrees.
Tips
A common mistake is to assume that interior angles on the same side of the transversal are congruent (equal), which is only true for alternate interior angles. Remember that same-side interior angles are supplementary.
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