Answer:
Explanation:
To find the measure of an angle, we need to set up an equation based on the given information. Let's call the angle "x".
According to the question, the angle is 420 less than three times its own supplement. The supplement of an angle is the angle that, when added to the given angle, equals 180 degrees.
Here are the steps to find the measure of the angle:
1. Write the equation based on the information given: x = 3(180 - x) - 420.
- The right side of the equation represents three times the supplement of the angle, and subtracting 420 indicates that it is 420 less than that value.
2. Simplify the equation: x = 540 - 3x - 420.
- Distribute the 3 to both terms inside the parentheses.
3. Combine like terms: x + 3x = 540 - 420.
- Add the x terms on the left side and subtract 420 from 540 on the right side.
4. Simplify further: 4x = 120.
- Combine like terms on both sides of the equation.
5. Solve for x by dividing both sides by 4: x = 30.
- Divide 120 by 4 to find the value of x.
Therefore, the measure of the angle is 30 degrees.