Question

Consecutive interior angles lines j and k are parallel. If m² = (4x - 1)° and m6 = (y - 31)° and m8 = 105°, what is the value of x and y?

Answer 1

By using the properties of consecutive interior angles on parallel lines and solving the corresponding equations, we determined the values to be x = 19 and y = 136.

Step-by-step explanation:

To solve for the values of x and y, we begin by recognizing that consecutive interior angles of parallel lines are supplementary, meaning they add up to 180 degrees. Given that lines j and k are parallel and m² and m¶ are consecutive interior angles, we can set up the equation (4x - 1)° + (y - 31)° = 180°. Additionally, we have the angle m¸ = 105°, which shares a linear pair with m¶, thus (y - 31)° = 105°.

Starting with m¸ = 105°, we solve for y:

• y - 31 = 105
• y = 136

Now, to solve for x, we substitute the value of y into the first equation:

• 4x - 1° + 136° - 31° = 180°
• 4x + 104 = 180
• 4x = 76
• x = 19

Thus, x = 19 and y = 136.