Question

Geometry helpppp plsssss -points-

Answer 1

Answer:

m < FBE is 62°

Step-by-step explanation:

Given the following facts:

BC bisects < FBE  

m < FBC = (10x - 9)°

m < CBE = (4x + 15)°

Since < FBC and < CBE are adjacent angles that have the same vertex, point B:

We can use the Angle Addition Postulate which states that If point B lies in the interior of < FBE then m < FBC + m < CBE = m < FBE.  

Essentially, the Angle Addition Postulate implies that the sum of the parts equal the whole.

To find the measure of < FBE:

Establish the following equality statement:

m < FBC = m < CBE

Substitute the given values into the equality statement:

    (10x - 9)° = (4x + 15)°

Combine like terms:

    10x - 9 = 4x + 15

Subtract 4x from both sides:

     10x - 4x - 9 = 4x - 4x + 15

    6x - 9 = 15

Add 9 to both sides:

    6x - 9 + 9 = 15 + 9

    6x = 24

Divide both sides by 6 to solve for x:

    6x/6 = 24/6

    x = 4

Now that we have the value for x, substitute 4 into the sum of the given values for < FBC and < CBE to solve for m < FBE:

     m < FBC + m < CBE = m < FBE

     (10x - 9)° +  (4x + 15)° = m < FBE

    [10(4) - 9]° + [4(4) + 15]° = m < FBE

    (40 - 9)° + (16 + 15)° = m < FBE

    31° + 31° = m < FBE

    62° = m < FBE

Therefore:

    m < FBC = 31°

    m < CBE = 31°

    m < FBE is 62°

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