if m<afb= 8x-6 and m<bfc = 14x+8, find the value of x so that <afc is a right angle..
Assuming that B is between A and C,
8x-6 + 14x+8 = 90
22x + 2 = 90
22x = 88
x = 4
To find the value of x that makes ∠AFC a right angle, we need to use the information given about the angles m<AFB and m<BFC in conjunction with the properties of angles in a triangle.
In a triangle, the sum of the interior angles is always 180 degrees. Therefore, we can set up the following equation:
m<AFB + m<BFC + m<AFC = 180 degrees (Equation 1)
From the information provided, we know that:
m<AFB = 8x - 6
m<BFC = 14x + 8
Substituting these values into Equation 1, we get:
(8x - 6) + (14x + 8) + m<AFC = 180
Simplifying the equation:
22x + 2 + m<AFC = 180
We also know that in a right triangle, one angle measures 90 degrees. Therefore, to make ∠AFC a right angle, we need:
m<AFC = 90 degrees
Substituting this into the above equation:
22x + 2 + 90 = 180
Simplifying further:
22x + 92 = 180
Subtracting 92 from both sides:
22x = 88
Finally, dividing both sides by 22:
x = 4
Therefore, the value of x that makes ∠AFC a right angle is x = 4.