Respuesta :

calculista

Answer:

[tex]x=5[/tex]

Step-by-step explanation:

step 1

Find the measure of angle EFD

In this problem I will assume that ABCD is a parallelogram

In a parallelogram opposite angles are congruent and consecutive angles are supplementary

so

[tex]m\ angle BCD=m\angle BED=51^o[/tex]

[tex]m\ angle FED=(1/2)m\angle BED=(1/2)51^o=25.5^o[/tex] --- > given problem

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

In the triangle EFD

[tex]m\ angle FED+m\ angle FDE+m\ angle EFD=180^o[/tex]

substitute the given values

[tex]25.5^o+55^o+m\ angle EFD=180^o[/tex]

[tex]80.5^o+m\ angle EFD=180^o[/tex]

[tex]m\ angle EFD=180^o-80.5^o[/tex]

[tex]m\ angle EFD=99.5^o[/tex]

step 2

Find the measure of angle EFB

we know that

[tex]m\angle EFB+m\angle EFD=180^o[/tex] ---> by supplementary angles

we have

[tex]m\ angle EFD=99.5^o[/tex]

substitute

[tex]m\angle EFB+99.5^o=180^o[/tex]

[tex]m\angle EFB=180^o-99.5^o[/tex]

[tex]m\angle EFB=80.5^o[/tex]

step 3

Find the value of x

Remember that the sum of the interior angles in any triangle must be equal to 180 degrees

so

In the triangle EBF

[tex]m\ angle BEF+m\ angle EFB+m\ angle EBF=180^o[/tex]

we have

[tex]m\angle BEF=m\ angle FED=25.5^o[/tex]

[tex]m\angle EFB=80.5^o[/tex]

[tex]m\angle EBF=(14x+4)^o[/tex]

substitute

[tex]25.5^o+80.5^o+(14x+4)^o=180^o[/tex]

solve for x

Combine like terms

[tex](14x+110)^o=180^o[/tex]

[tex]14x=180-110[/tex]

[tex]14x=70[/tex]

[tex]x=5[/tex]

The value of x is = 5

Suppose that BCDE is a parallelogram.

According to the given question ;

In a parallelogram Opposite sides are congruent. Opposite angles are congruent. Consecutive angles are supplementary. The diagonals bisect each other.  

So ,

m∠BCD= m∠BED = 51°

m∠FED = [tex]\frac{1}{2} m[/tex]∠BED

              = [tex]\frac{1}{2} ( 51 )[/tex]

              = 25.5 °

Remember that the sum of the all interior angles in any triangle must be equal to 180° degrees.

m∠FED + m∠FDE + m∠EFD = 180°

22.5° + 55° + m∠EFD = 180°

m∠EFD = 180° - 80.5°

m∠EFD = 99.5°

Now,

TO find measure of angle EFB

we know that

m∠EFP + m∠EFD = 180°

By supplementary angles The two angles are said to be supplementary angles when they add up to 180°.

we have,

m∠EFD =99.5°

Substitute

m∠EFB + 99.5° = 180°

m∠EFB = 80.5°

Again by the property the sum of all the interior angle  in the angle is 180°

In the,

m∠BEF + m∠EFB + m∠EBF = 180°

we have

m∠BEF = m ∠FED = 25.5°

m∠EFB = 80.5°

m∠EBF = ( 14x + 4 )°

substitute the values

25.5 + 80.5 + ( 14x+4) = 180

106 + 14x + 4 = 180

110 + 14x = 180

14x = 180-110

14x = 70

x =[tex]\frac{70}{14}[/tex]

x = 5

The value of x is 5 .

For the more information about parallelogram properties click the link given below .

https://brainly.com/question/22106495

 

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