![a=125^o](/tpl/images/0446/8197/b9906.png)
![b=55^o](/tpl/images/0446/8197/d0828.png)
![c=55^o](/tpl/images/0446/8197/cd7d2.png)
![d=55^o](/tpl/images/0446/8197/1c8bf.png)
![e=125^o](/tpl/images/0446/8197/fe2a7.png)
![f=55^o](/tpl/images/0446/8197/5ab15.png)
Step-by-step explanation:
step 1
Find the value of x
we know that
----> by alternate interior angles
solve for x
Group terms
![2x-x=75-25](/tpl/images/0446/8197/a8e6d.png)
![x=50](/tpl/images/0446/8197/53965.png)
step 2
Find the measure of angle a
we know that
----> by vertical angles
substitute the value of x
![a=(50+75)=125^o](/tpl/images/0446/8197/099c4.png)
step 3
Find the measure of angle b
we know that
----> by supplementary angles (form a linear pair)
we have
![a=125^o](/tpl/images/0446/8197/b9906.png)
substitute
![125^o+b=180^o](/tpl/images/0446/8197/df086.png)
![b=180^o-125^o=55^o](/tpl/images/0446/8197/06a57.png)
step 4
Find the measure of angle c
we know that
----> by vertical angles
we have
![b=55^o](/tpl/images/0446/8197/d0828.png)
therefore
![c=55^o](/tpl/images/0446/8197/cd7d2.png)
step 5
Find the measure of angle d
we know that
----> by corresponding angles
we have
![b=55^o](/tpl/images/0446/8197/d0828.png)
therefore
![d=55^o](/tpl/images/0446/8197/1c8bf.png)
step 6
Find the measure of angle e
we know that
----> by alternate exterior angles
we have
![a=125^o](/tpl/images/0446/8197/b9906.png)
therefore
![e=125^o](/tpl/images/0446/8197/fe2a7.png)
step 7
Find the measure of angle f
we know that
----> by vertical angles
we have
![d=55^o](/tpl/images/0446/8197/1c8bf.png)
therefore
![f=55^o](/tpl/images/0446/8197/5ab15.png)