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g100num [7]
2 years ago
5

Find the measure of each of the angles. Don’t forget to label your answer

Mathematics
1 answer:
user100 [1]2 years ago
4 0

Answer:

a=125^o

b=55^o

c=55^o

d=55^o

e=125^o

f=55^o

Step-by-step explanation:

step 1

Find the value of x

we know that

(2x+25)^o=(x+75)^o ----> by alternate interior angles

solve for x

Group terms

2x-x=75-25

x=50

step 2

Find the measure of angle a

we know that

a=(x+75)^o ----> by vertical angles

substitute the value of x

a=(50+75)=125^o

step 3

Find the measure of angle b

we know that

a+b=180^o ----> by supplementary angles (form a linear pair)

we have

a=125^o

substitute

125^o+b=180^o

b=180^o-125^o=55^o

step 4

Find the measure of angle c

we know that

c=b ----> by vertical angles

we have

b=55^o

therefore

c=55^o

step 5

Find the measure of angle d

we know that

d=b ----> by corresponding angles

we have

b=55^o

therefore

d=55^o

step 6

Find the measure of angle e

we know that

e=a ----> by alternate exterior angles

we have

a=125^o

therefore

e=125^o

step 7

Find the measure of angle f

we know that

f=d ----> by vertical angles

we have

d=55^o

therefore

f=55^o

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