Answer:
[tex]a=125^o[/tex]
[tex]b=55^o[/tex]
[tex]c=55^o[/tex]
[tex]d=55^o[/tex]
[tex]e=125^o[/tex]
[tex]f=55^o[/tex]
Step-by-step explanation:
step 1
Find the value of x
we know that
[tex](2x+25)^o=(x+75)^o[/tex] ----> by alternate interior angles
solve for x
Group terms
[tex]2x-x=75-25[/tex]
[tex]x=50[/tex]
step 2
Find the measure of angle a
we know that
[tex]a=(x+75)^o[/tex] ----> by vertical angles
substitute the value of x
[tex]a=(50+75)=125^o[/tex]
step 3
Find the measure of angle b
we know that
[tex]a+b=180^o[/tex] ----> by supplementary angles (form a linear pair)
we have
[tex]a=125^o[/tex]
substitute
[tex]125^o+b=180^o[/tex]
[tex]b=180^o-125^o=55^o[/tex]
step 4
Find the measure of angle c
we know that
[tex]c=b[/tex] ----> by vertical angles
we have
[tex]b=55^o[/tex]
therefore
[tex]c=55^o[/tex]
step 5
Find the measure of angle d
we know that
[tex]d=b[/tex] ----> by corresponding angles
we have
[tex]b=55^o[/tex]
therefore
[tex]d=55^o[/tex]
step 6
Find the measure of angle e
we know that
[tex]e=a[/tex] ----> by alternate exterior angles
we have
[tex]a=125^o[/tex]
therefore
[tex]e=125^o[/tex]
step 7
Find the measure of angle f
we know that
[tex]f=d[/tex] ----> by vertical angles
we have
[tex]d=55^o[/tex]
therefore
[tex]f=55^o[/tex]
