Question

Assume lines p and q intersect to form adjacent angles 1 and 2. If m∠1 = (7x + 6)° and m∠2 = (8x – 60)°, find the value of x such that line p is perpendicular to line q.

A) x = 15
B) x = 10
C) x = 6
D) x = 9

Answer 1

Upon calculation, the value of x is found to be 9.6, which doesn't match any of the provided options. It's suggested that the student rechecks the values and the answer choices in the question for accuracy.

Step-by-step explanation:

To find the value of x such that line p is perpendicular to line q, we must know that adjacent angles formed by perpendicular lines sum up to 90 degrees. Given that m∠1 = (7x + 6)° and m∠2 = (8x – 60)°, we set up the equation:

• (7x + 6) + (8x - 60) = 90

Combining like terms, we get:

• 15x - 54 = 90
• 15x = 144
• x = 144 / 15
• x = 9.6

However, since 9.6 is not an option, we may have made a mistake. Let's retry the calculation.

• 15x - 54 = 90
• 15x = 144
• x = 144 / 15
• x = 9.6 (This appears to be an error because 9.6 is not one of the choices provided)

Let's divide 144 by 15 again to verify:

• x = 144 / 15
• x = 9.6 (This verification confirms the previous result.)

It seems there may be an issue with the provided answer choices if our calculations are correct. As a tutor, I expect the student to recheck the values and the answer choices given in the question to ensure there's no typographical error.