Answer:
x = 11, y = 41
Step-by-step explanation:
The angles m < (4x + 6)° and m < (6x - 16)° are alternate interior angles that do not have a common vertex, and lie on the alternate sides of the transversal. Alternate interior angles also have the same measure.
Additionally, the exterior angle, m < (y + 9)° and the interior angle, m < (4x + 5)° are corresponding angles that have the same measure.
To solve for the values of x we can establish the following equality statement:
m < (4x + 6)° = m < (6x - 16)°
4x + 6 = 6x - 16
Subtract 4x from both sides:
4x - 4x + 6 = 6x - 4x - 16
6 = 2x - 16
Add 16 to both sides:
16 + 6 = 2x - 16 + 16
22 = 2x
Divide both sides by 2:
22/2 = 2x/2
11 = x
Now that we have the value of x = 11, we can substitute this value into the following equation to solve for y:
4x + 6 = y + 9
4(11) + 6 = y + 9
44 + 6 = y + 9
50 = y + 9
Subtract 9 from both sides:
50 - 9 = y + 9 - 9
41 = y
Double-check whether we have the correct value for x:
m < (4x + 6)° = m < (6x - 16)°
4(11) + 6 = 6(11) - 16
50 = 50 (True statement. This means that we have the correct value for x).
Do the same thing for the following to verify whether we have the correct value for y:
m < (4x + 6)° = m < (y + 9)°
4(11) + 6 = 41 + 9
50 = 50 (True statement).
Therefore, the correct answers are: x = 11, y = 41.
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