Question

In a geometric context, if the measure of angle ∠4 is represented by (3x + 7) degrees, and the measure of angle ∠5 is represented by (9x - 43) degrees, calculate the measure of angle ∠UPS."

Answer 1

To find the measure of angle ∠UPS, set up an equation using the measures of angles ∠4 and ∠5. Simplify the equation and substitute the values to solve for ∠UPS.

Step-by-step explanation:

To calculate the measure of angle ∠UPS, we need to find the values of x that represent the measures of angles ∠4 and ∠5. Then we can substitute these values into the equation to solve for the measure of angle ∠UPS.

1. Given: ∠4 = (3x + 7) degrees and ∠5 = (9x - 43) degrees
2. Set up an equation: ∠4 + ∠5 + ∠UPS = 180 degrees (sum of angles in a triangle)
3. Substitute the values of ∠4 and ∠5 into the equation: (3x + 7) + (9x - 43) + ∠UPS = 180 degrees
4. Simplify the equation: 12x - 36 + ∠UPS = 180 degrees
5. Combine like terms: 12x + ∠UPS = 216 degrees
6. Subtract 12x from both sides: ∠UPS = 216 degrees - 12x

Therefore, the measure of angle ∠UPS is 216 degrees - 12x.