Answer:
ASA theorem tells us angle EXF congruent to angle EXD
Hello! What you're seeing in these images are two parallel lines cut by a transversal. There are many relationships between angles here.
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Problem g: What you are seeing here is alternate interior angles - they are both on the inside of the lines, and are on opposite sides of the transversal. These angles are proven to always measure the same thing.
Therefore, 8x - 4 = 60. Use this equation, and solve.
8x - 4 = 60
8x = 64
x = 8
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Problem h: Here, you are seeing corresponding angles. When you look at the two intersection points, these two angles are located "between the same sides". These angles are also proven to always measure the same.
Therefore, 6x = 5x + 10. Use this equation, and solve.
6x = 5x + 10
x = 10
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Problem i: These are alternate exterior angels. These are located on opposite ends of the transversal, and are on the outside of the parallel lines. These angles also always measure the same.
Therefore, -1 + 14x = 12x + 17. Now solve.
-1 + 14x = 12x + 17
2x = 18
x = 9
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Therefore, your three answers are x = 8, x = 10, and x = 9.
Hope this helps!
