Use an Algebraic Equation to Find the Measure of Each Angle That is Represented in Terms of x

To find the measure of each angle in a given geometric figure, we can set up an algebraic equation based on the relationships of the angles. Let’s assume we have a triangle where the angles are represented as follows:

• First angle: 2x
• Second angle: 3x
• Third angle: x + 10

We know that the sum of the angles in a triangle is always 180 degrees. Therefore, we can write the equation as:

2x + 3x + (x + 10) = 180

Simplifying this equation gives:

6x + 10 = 180

Next, we subtract 10 from both sides:

6x = 170

Now, we divide both sides by 6:

x = rac{170}{6} 	ext{ or } x 	ext{ is approximately } 28.33

With the value of x, we can now find each angle:

• First angle: 2x = 2(28.33) ext{ or approximately } 56.67 degrees
• Second angle: 3x = 3(28.33) ext{ or approximately } 85 degrees
• Third angle: x + 10 = 28.33 + 10 = 38.33 degrees

In conclusion, by setting up an algebraic equation relating the angles and solving for x, we have determined the measures of each angle in the triangle.