Question

(SAT Prep) Find the value of x in each of the the following exercises:​

Answer 1

x=115 degrees

Explanation:

see the attached figure to better understand the problem

Remember that

The sum of the interior angles in a triangle must be equal to 180 degrees

In the triangle AEF

we have

----> given problem

step 1

Find the measure of angle AFE

we know that

-----> by corresponding angles

---> by supplementary angles (form a linear pair)

so

step 2

Find the measure of angle AEF

we know that

---> by supplementary angles (form a linear pair)

----> given problem

so

step 3

Find the value of x

Remember

we have

substitute

solve for x

Answer 2

`x=115^o`

Explanation:

see the attached figure to better understand the problem

Remember that

The sum of the interior angles in a triangle must be equal to 180 degrees

In the triangle AEF

`m\angle EAF+m\angle AEF+m\angle AFE=180^o`

we have

`m\angle EAF=50^o` ----> given problem

step 1

Find the measure of angle AFE

we know that

`m\angle AFG=m\angle C=x^o` -----> by corresponding angles

`m\angle AFE+m\angle AFG=180^o` ---> by supplementary angles (form a linear pair)

so

`m\angle AFE+x=180^o`

`m\angle AFE=(180-x)^o`

step 2

Find the measure of angle AEF

we know that

`m\angle AEF+m\angle DEA=180^o` ---> by supplementary angles (form a linear pair)

`m\angle DEA=x^o` ----> given problem

so

`m\angle AEF+x^o=180^o`

`m\angle AEF=(180-x)^o`

step 3

Find the value of x

Remember

`m\angle EAF+m\angle AEF+m\angle AFE=180^o`

we have

`m\angle EAF=50^o`

`m\angle AFE=(180-x)^o`

`m\angle AEF=(180-x)^o`

substitute

`50^o+(180-x)^o+(180-x)^o=180^o`

solve for x

`410-2x=180`

`2x=410-180`

`2x=230`

`x=115^o`