Question

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

Answer 1

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

$f=55^o$