Determine the values of x and y in the diagram and use them to determine the measures of the eight angles

Part 1)

Part 2)

Part 3)

Part 4)

Part 5)

Part 6)

Part 7)

Part 8)

Part 9)

Part 10)

Step-by-step explanation:

see the attached figure with letters to better understand the problem

Part 1) Determine the value of x

we know that

----> by alternate exterior angles

substitute the given values

solve for x

Part 2) Determine the value of y

we know that

----> by supplementary angles (consecutive interior angles)

substitute the given values

solve for y

Part 3) Find the measure of angle a

we have

substitute the value of x

Part 4) Find the measure of angle b

we know that

----> by supplementary angles (consecutive interior angles)

we have

substitute

Part 5) Find the measure of angle c

we know that

----> by vertical angles

we have

therefore

Part 6) Find the measure of angle d

we know that

----> by vertical angles

we have

therefore

Part 7) Find the measure of angle e

we know that

----> by corresponding angles

we have

therefore

Part 8) Find the measure of angle f

we know that

----> by corresponding angles

we have

therefore

Part 9) Find the measure of angle g

we know that

----> by corresponding angles

we have

therefore

Part 10) Find the measure of angle h

we know that

----> by corresponding angles

we have

therefore