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Answer:

Part 1) [tex]x=8[/tex]

Part 2) [tex]y=12[/tex]

Part 3) [tex]m\angle a=105^o[/tex]

Part 4) [tex]m\angle b=75^o[/tex]

Part 5) [tex]m\angle c=105^o[/tex]

Part 6) [tex]m\angle d=75^o[/tex]

Part 7) [tex]m\angle e=105^o[/tex]

Part 8) [tex]m\angle f=75^o[/tex]

Part 9) [tex]m\angle g=105^o[/tex]

Part 10) [tex]m\angle h=75^o[/tex]

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

[tex]m\angle a=m\angle g[/tex] ----> by alternate exterior angles

substitute the given values

[tex](17x-31)^o=(12x+9)^o[/tex]

solve for x

[tex]17x-12x=9+31\\5x=40\\x=8[/tex]

Part 2) Determine the value of y

we know that

[tex]m\angle c+m\angle d=180^o[/tex] ----> by supplementary angles (consecutive interior angles)

substitute the given values

[tex](7y+21)^o+(5y+15)^o=180^o[/tex]

solve for y

[tex](12y+36)^o=180^o[/tex]

[tex]12y=180-36[/tex]

[tex]12y=144[/tex]

[tex]y=12[/tex]

Part 3) Find the measure of angle a

we have

[tex]m\angle a=(17x-31)^o[/tex]

substitute the value of x

[tex]m\angle a=(17(8)-31)=105^o[/tex]

Part 4) Find the measure of angle b

we know that

[tex]m\angle a+m\angle b=180^o[/tex] ----> by supplementary angles (consecutive interior angles)

we have

[tex]m\angle a=105^o[/tex]

substitute

[tex]105^o+m\angle b=180^o[/tex]

[tex]m\angle b=180^o-105^o[/tex]

[tex]m\angle b=75^o[/tex]

Part 5) Find the measure of angle c

we know that

[tex]m\angle c=m\angle a[/tex] ----> by vertical angles

we have

[tex]m\angle a=105^o[/tex]

therefore

[tex]m\angle c=105^o[/tex]

Part 6) Find the measure of angle d

we know that

[tex]m\angle d=m\angle b[/tex] ----> by vertical angles

we have

[tex]m\angle b=75^o[/tex]

therefore

[tex]m\angle d=75^o[/tex]

Part 7) Find the measure of angle e

we know that

[tex]m\angle e=m\angle a[/tex] ----> by corresponding angles

we have

[tex]m\angle a=105^o[/tex]

therefore

[tex]m\angle e=105^o[/tex]

Part 8) Find the measure of angle f

we know that

[tex]m\angle f=m\angle b[/tex] ----> by corresponding angles

we have

[tex]m\angle b=75^o[/tex]

therefore

[tex]m\angle f=75^o[/tex]

Part 9) Find the measure of angle g

we know that

[tex]m\angle g=m\angle c[/tex] ----> by corresponding angles

we have

[tex]m\angle c=105^o[/tex]

therefore

[tex]m\angle g=105^o[/tex]

Part 10) Find the measure of angle h

we know that

[tex]m\angle h=m\angle d[/tex] ----> by corresponding angles

we have

[tex]m\angle d=75^o[/tex]

therefore

[tex]m\angle h=75^o[/tex]

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