Real Life Parallel Lines And Transversals

Angle 3 and angle 6 are alternate exterior angles. Alternate exterior angles are formed when a transversal intersects two parallel lines. In this case, the transversal is the line formed by the edge of the photo and the two parallel lines are the edges of the airport building. Angle 3 and angle 6 are on opposite sides of the transversal and are congruent, making them alternate exterior angles.

The measure of angle 2 is 60 degrees because the pained lines that separate parking spaces are parallel, which means that angle 1 and angle 2 are corresponding angles. Corresponding angles that are formed by a transversal and parallel lines are congruent, so if angle 1 is 60 degrees, then angle 2 must also be 60 degrees.

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Since Redding Lane and Creek Road are parallel streets, angle 1 and angle 2 are corresponding angles. Corresponding angles are congruent when the two parallel lines are intersected by a transversal. Therefore, angle 2 must also be 118 degrees.

The image shows the reflection angles of a ball bouncing off the walls of a rectangular table. The given angles are:

64° where the ball hits the side wall.

58° at another point.

Using the property of angles of incidence and reflection, we know that these angles should be equal at each bounce if it is a perfect reflection.

Therefore, at the point marked x, the angle should be equal to the angle at the previous bounce.

From the given angles, it is clear that the angle x must be equal to 64° because it follows the same line of incidence and reflection from the previous bounce point.

So, the value of x is 64°.

The measure of angle 1 is 100 degrees because the question states that the letters are slanted at an 80-degree angle. Since angle 1 is the complement of the slanted angle, it must be 100 degrees (180 - 80 = 100).

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The correct answer is 8 because angle 3 is equal to 4y + 30 and angle 7 is equal to 7y + 6. By substituting the value of angle 3 into angle 7, we get 4y + 30 = 7y + 6. Solving this equation, we find that y = 8. Therefore, angle 3 is equal to 4(8) + 30 = 62, which is the same as angle 7.

Since angle 1 is equal to 85 and angle 4 is equal to 2x - 17, we can set up an equation to solve for x. We have 2x - 17 = 85. Adding 17 to both sides gives us 2x = 102. Dividing both sides by 2 gives us x = 51. Therefore, the correct answer is 56.

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1. Identify the relationship between the angles:

The angles (3x - 15)° and (y + 25)° are corresponding angles. Corresponding angles are formed when a transversal line intersects two parallel lines. They are located in the same relative position at each intersection.  

2. Use the property of corresponding angles:

When a transversal intersects two parallel lines, corresponding angles are congruent (equal). Therefore:

3x - 15 = y + 25

3. Find the value of x:

The angle marked 105° and the angle (3x - 15)° are supplementary angles. Supplementary angles add up to 180°. Therefore:

105 + (3x - 15) = 180 3x + 90 = 180 3x = 90 x = 30

4. Substitute the value of x to find y:

3(30) - 15 = y + 25 90 - 15 = y + 25 75 = y + 25 y = 50

Therefore, the value of y is 50.