Question

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

Answer 1

Answer:

$x=115^o$

Step-by-step 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

$410-2x=180$

$2x=410-180$

$2x=230$

$x=115^o$

Answer 2

Answer:

x=115 degrees

Step-by-step 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