Final answer:
The value of x is 5, and using this value, the measure of angle 6 can be calculated as 30 degrees by substituting x into the given expression for m∠6.
Step-by-step explanation:
The student's question concerns finding the value of x and the measure of angle 6, given that angle 5 is supplementary to angle 6, with m∠5 = 40x − 50 and m∠6 = 5x + 5. Two angles are supplementary if the sum of their measures is 180 degrees. Therefore, the equation to solve is (40x − 50) + (5x + 5) = 180, which simplifies to 45x − 45 = 180.
To find the value of x, we add 45 to both sides of the equation, getting 45x = 225. Then, we divide both sides by 45, resulting in x = 5. With the value of x determined, we can substitute it back into the equation for m∠6 to find the measure of angle 6: m∠6 = 5(5) + 5 = 30 degrees.