Respuesta :
Answer:
The solution in the attached figure
[tex]m<A=43\°[/tex]
[tex]m<B=137\°[/tex]
[tex]m<C=43\°[/tex]
[tex]m<D=43\°[/tex]
[tex]m<E=137\°[/tex]
[tex]m<F=137\°[/tex]
[tex]m<G=43\°[/tex]
Step-by-step explanation:
see the attached figure with letters to better understand the problem
Part 1) Find the measure of angle A
we know that
[tex]m<A+137\°=180\°[/tex] ------> by supplementary angles
so
[tex]m<A=180\°-137\°=43\°[/tex]
Part 2) Find the measure of angle B
we know that
[tex]m<B=137\°[/tex] ------> by vertical angles
Part 3) Find the measure of angle C
we know that
[tex]m<C=m<A[/tex] ------> by vertical angles
so
[tex]m<C=43\°[/tex]
Part 4) Find the measure of angle D
we know that
[tex]m<D=m<A[/tex] ------> by corresponding angles
so
[tex]m<D=43\°[/tex]
Part 5) Find the measure of angle E
we know that
[tex]m<E+m<D=180\°[/tex] ------> by supplementary angles
so
[tex]m<E+43\°=180\°[/tex]
[tex]m<E=180\°-43\°=137\°[/tex]
Part 6) Find the measure of angle F
we know that
[tex]m<F=m<E[/tex] ------> by vertical angles
so
[tex]m<F=137\°[/tex]
Part 6) Find the measure of angle G
we know that
[tex]m<G=m<D[/tex] ------> by vertical angles
so
[tex]m<G=43\°[/tex]