Final answer:
When two lines are parallel, their corresponding angles are congruent. By setting the given angle measures equal to each other, we can solve for x and find the values of the angles. Then, by substituting x into one of the angle measures, we can find the value of that angle. Finally, we can use one of the other angle measures to solve for y and find its value.
Step-by-step explanation:
When two lines are parallel, their corresponding angles are congruent. In this case, we have angles 3 and 6, which are corresponding angles. Since the measure of angle 3 is given as 5x - 7 and the measure of angle 6 is given as 3x + 17, we can set these two expressions equal to each other and solve for x.
5x - 7 = 3x + 17
2x = 24
x = 12
Now that we know x, we can substitute it into one of the angle measures, such as angle 3, to find its value.
m∠3 = 5x - 7 = 5(12) - 7 = 53
Therefore, x = 12 and the value of angle 3 is 53.
To find the value of y, we can use angle 4, which is also a corresponding angle to angles 3 and 6. Angle 4 is given as 4y + 3. Since we solved for x earlier, we can now substitute it into this equation and solve for y.
4y + 3 = 4(12) + 3 = 51
Therefore, x = 12 and y = 51.