Final answer:
To find the measure of angle 8, corresponding angles are leveraged due to parallel lines, leading to solving the equation 12x + 11 = 10x + 15. Upon finding x, it is substituted back into the expression for m∠8 to obtain the correct measure, which is 35 degrees. None of the provided choices match this correct measure.
Step-by-step explanation:
The student is tasked with finding the measure of m∠8 given that lines a and b are parallel and m∠1 is expressed as 12x + 11 degrees, while m∠8 is given as 10x + 15 degrees. Since lines a and b are parallel, corresponding angles are equal which means that m∠1 = m∠8. Therefore, the equations 12x + 11 = 10x + 15 can be set up, and solving for x gives us the value to calculate m∠8.
First, subtract 10x from both sides to isolate x on one side of the equation:
2x + 11 = 15. Next, subtract 11 from both sides:
2x = 4. Now, divide both sides by 2 to solve for x:
x = 2. Substituting x = 2 into the original equation for m∠8 gives us m∠8 = 10(2) + 15, which simplifies to m∠8 = 20 + 15 and therefore m∠8 = 35 degrees. Hence, none of the provided choices (A, B, C, D) are correct for m∠8.