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Answer:
70°; alternate exterior angles theorem
Step-by-step explanation:
The line at the gate is a "transversal" crossing the (parallel) skis. The angles marked 1 and 70° are outside the parallel lines and on opposite sides of the transversal. They are called "alternate exterior* angles."
When the lines are parallel, alternate exterior angles are congruent, so ∠1 = 70°. This observation works both ways: if the angles are congruent, the lines are parallel. The observation is called the Alternate Exterior Angles Theorem.
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* angles at a transversal are classified as "interior" (between the parallel lines) or "exterior" (outside the parallel lines). The are also classified as "same-side" or "sequential" (on the same side of the transversal), or "alternate" (on opposite sides of the transversal). Here, the angles are exterior and alternate.
