Two railroad tracks cross each other. If the measure of angle 1 is 3 times the measure of angle 2. What are the measures of angles 1,2,3, and 4? Explain and show your work please.

I assume the gaps form something like a circle. Based on this, you have 3x + x = 180, since we are just finding the measures of the circle. 4x = 180. x = 45

45 is angle 2.
135 is angle 1.

So, angles 1 and 3 are 135 degrees each and angles 2 and 4 are 45 degrees.

divide 1.45 by 5. explain how you got your answer in a complete sentence

At right are several roads that will be built as part of a new hospital complex. The angel at which road 1 meets road 2 is twice the measure of the angle at which road 2 meets road 3.Fill the missing angle measure on the diagram.Write and solve equation to justify your answer

To determine the measures of angles 1, 2, 3, and 4, we can start by understanding the geometry of intersecting lines. When two lines intersect, they form two pairs of opposite angles. In this case, angles 1 and 3 form one pair of opposite angles, while angles 2 and 4 form the other pair.

Let's assign a variable, say 'x', to the measure of angle 2. Since angle 1 is stated to be three times the measure of angle 2, angle 1 can be represented as 3x.

Considering the relationship between opposite angles, angle 3 must have the same measure as angle 1 (vertical angles theorem). Therefore, angle 3 will also be 3x.

Furthermore, by applying the properties of angles formed when two lines are crossed by a transversal, we know that angles 1 and 3 form a linear pair with angle 4. A linear pair consists of two adjacent angles that together form a straight line, which means that they add up to 180 degrees.

So, to find angle 4, we subtract the sum of angles 1 and 3 from 180 degrees:
Angle 4 = 180° - (angle 1 + angle 3) = 180° - (3x + 3x) = 180° - 6x.

In summary:
Angle 1 = 3x
Angle 2 = x
Angle 3 = 3x
Angle 4 = 180° - 6x

Now, we have expressions for each angle in terms of 'x.' To find specific angle measures, we need additional information, such as the value of 'x' or the relationship between angle 1 and angle 2.