Final answer:
To find the value of x for the angles P and S, we add the given expression for P with the measure of S and set it equal to the sum of both angles. After simplifying the equation, the value of x is determined to be 6.
Step-by-step explanation:
To find the value of x, we need to solve the equation that represents the sum of the measures of angle P and angle S. The measure of angle P is given as (5x+30)° and the measure of angle S is given as 80°. So, we have the equation (5x+30) + 80 = 140. Simplifying this equation, we get 5x + 110 = 140. Subtracting 110 from both sides, we get 5x = 30. Finally, dividing both sides by 5, we find that x = 6. Therefore, the value of x is 6.
The student has presented a problem involving two angles, P and S, where the sum of their measures is 140°. They have given the measure of angle P as (5x+30)° and informed us that the measure of angle S is 80°. To find the value of x, we set up an equation: (5x + 30) + 80 = 140. Solving for x, we subtract 80 and 30 from both sides, getting 5x = 30. Dividing both sides by 5, x equals 6. Therefore, the value of x is 6.