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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