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So the angle measure for ∠L is 22.5° when two parallel lines cut by a transversal.
In geometry, a transversal is a line that intersects two or more other lines in a plane. When a transversal intersects two parallel lines, it creates a series of corresponding angles, alternate angles, and interior angles, which have specific relationships and properties.
Here,
Since lines a and b are parallel, we know that alternate interior angles are congruent. Therefore, we have:
∠F = ∠L + 180° - 135°
Simplifying this expression, we get:
∠F = ∠L + 45°
Substituting the value of ∠F as 67.5°, we can solve for ∠L:
67.5° = ∠L + 45°
22.5° = ∠L
The relationship between ∠F and ∠L is that they are supplementary angles, meaning they add up to 180°. This is because they are on opposite sides of the transversal and both intersect with the same parallel lines a and b.
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Complete question:
Two parallel lines cut by a transversal. For our safety, it is important that drivers recognize a stop sign immediately. Stop signs are made with exact side and angle measurements to form a regular octagon. They are red so they are easy to see. The three lines drawn below are straight lines. Lines a and b are parallel. a) The stop sign is a regular octagon, so the measure of ∠F must be 67.5°. What is the angle measure for ∠L? Describe the relationship between ∠F and ∠L. (1 point)
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