Subjects geometry

Parallel Lines Angles 671515

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1. **Stating the problem:** We have two parallel lines AB and CD with a transversal intersecting them, creating several angles. Given angles at points M and N on line CD are 98° and 73° respectively. We need to find the measures of angles 1 and 2 on line AB. 2. **Relevant rules and formulas:** When a transversal crosses parallel lines, corresponding angles are equal, alternate interior angles are equal, and consecutive interior angles are supplementary (sum to 180°). 3. **Identify angles:** Angles 98° and 73° are on line CD. Angles 1 and 2 are on line AB. Since AB is parallel to CD, angles on AB correspond or relate to those on CD via the transversal. 4. **Find angle 1:** Angle 1 corresponds to angle 98° (alternate interior angles), so angle 1 = 98°. 5. **Find angle 2:** Angle 2 corresponds to angle 73° (alternate interior angles), so angle 2 = 73°. 6. **Summary:** - Angle 1 = 98° - Angle 2 = 73° These follow from the properties of parallel lines and a transversal.
A B C D R S M N 1 2 98° 73°