Question

"Two lines intersect to form a linear pair of congruent angles. The measure of one angle is (6x + 42) and

the measure of the other angle is
(9y/4)
. Find the values of x and y."

Answer 1

To find the values of x and y, set up an equation using the given angle measures and use algebraic methods to solve for the variables.

Step-by-step explanation:

To find the values of x and y, we need to set up an equation using the given information about the angles. Since the angles form a linear pair, their measures add up to 180 degrees. So we have the equation:

(6x + 42) + (9y/4) = 180

To solve for x and y, we can simplify the equation and then solve for one variable in terms of the other. Let's multiply every term by 4 to get rid of the fraction:

24x + 168 + 9y = 720

Next, let's combine like terms:

24x + 9y = 720 - 168

24x + 9y = 552

Now, we can solve for x in terms of y by isolating x:

24x = 552 - 9y

x = (552 - 9y)/24

Similarly, we can solve for y in terms of x:

9y = 552 - 24x

y = (552 - 24x)/9

These two equations represent the values of x and y in terms of each other.