Question

Find the value of x. Then find the angle measures of the polygon.

angles of the polygon:

1/3x, (x-20), (x-10), 40

sum of the angle measures: 360

Answer 1

The value of x is found by setting the sum of the polygon's angles to 360 degrees and solving the resulting equation. The value of x is 262.5, and the individual angles of the polygon are 87.5°, 242.5°, 252.5°, and 40°.

Step-by-step explanation:

To find the value of x, we first recognize that the angles of a polygon sum up to 360 degrees. We are given the angles in terms of x, which are 1/3x, (x-20), (x-10), and 40. Adding all these angles together and setting them equal to 360 will help us solve for x:

1. Write the equation: (1/3)x + (x - 20) + (x - 10) + 40 = 360.
2. Combine like terms: (1 + 1/3)x = 360 + 20 + 10 - 40.
3. Simplify: (4/3)x = 350.
4. Multiply both sides by the reciprocal of (4/3) to solve for x: x = 350 * (3/4), which gives us x = 262.5.
5. Now, we can find the individual angle measures: 1/3(262.5), 262.5 - 20, 262.5 - 10, and 40.
6. Calculate each angle: 87.5°, 242.5°, 252.5°, and 40°.

Therefore, the value of x is 262.5, and the angle measures of the polygon are 87.5°, 242.5°, 252.5°, and 40°.

Answer 2

Just sum it all together to get the answer -----------> (x-10)