Question

In this picture, m∠TPU = 40° and m∠UPS = (5x + 8)°. If ∠TPU and ∠UPS are supplementary angles, then what is the value of x?

Answer 1

Since ∠TPU and ∠UPS are supplementary angles, the sum of their measures is equal to 180°. Therefore, we have the equation:

m∠TPU + m∠UPS = 180°

Substituting the given values, we have:

40° + (5x + 8)° = 180°

Simplifying the equation, we have:

5x + 48 = 180

Subtracting 48 from both sides of the equation, we have:

5x = 132

Finally, dividing both sides of the equation by 5, we have:

x = 26.4

Therefore, the value of x is 26.4.