Two lines intersect to form angle 1 comma space angle 2 comma space angle 3 comma space a n d space angle 4. The measure of angle 3

is 3 times the measure of angle 1 and m angle 1 equal m angle 2. Find the measure of each angle. Label your answers.

To find the measures of angles 1, 2, 3, and 4, we can use the given information and some properties of intersecting lines. Let's break down the problem step by step:

Step 1: Identify what we know:
- Angle 3 is three times the measure of Angle 1.
- The measure of Angle 1 is equal to the measure of Angle 2.

Step 2: Assign variables:
Let's assign a variable for Angle 1. We'll call it "x".

Step 3: Express the measures of the other angles using the variable:
- Angle 3 is three times the measure of Angle 1, so its measure is 3x.
- Angle 2 has the same measure as Angle 1, so its measure is also x.

Step 4: Use the fact that the angles around a point add up to 360 degrees:
The angles around a point (in this case, the intersection) add up to 360 degrees. Therefore, the sum of Angle 1, Angle 2, Angle 3, and Angle 4 is 360 degrees.

Step 5: Write an equation and solve for the variable:
We have:
Angle 1 + Angle 2 + Angle 3 + Angle 4 = 360 degrees
x + x + 3x + Angle 4 = 360
5x + Angle 4 = 360

Step 6: Solve for the variable:
Since we don't have any information about Angle 4, we cannot solve for the variable "x" directly. However, we can still find the value of x in terms of Angle 4.

Step 7: Substitute the value of x into the equation:
5x + Angle 4 = 360
5x = 360 - Angle 4
x = (360 - Angle 4) / 5

Step 8: Summary of the measures of each angle:
- Angle 1 (x)
- Angle 2 (x)
- Angle 3 (3x)
- Angle 4 (Angle 4)

To find the exact measures of the angles, we need to know the degree measure of Angle 4.