Question

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

A=
B=
C=
D=
E=
F=

Answer 1

`a=125^o\\b=55^o\\c=55^o\\d=55^o\\e=125^o\\f=55^o`

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`