Question

find the value of x.

x =
submit

Explanation:

Step1: Use the property of angles around a point

The sum of angles around point \(F\) is \(180^{\circ}\). We know that \(\angle BFD = 90^{\circ}\) (right - angle) and \(\angle BFC=26^{\circ}\).
The angle \(\angle AFE=(16x)^{\circ}\).
We can use the equation \((16x)+26 + 90=180\) (since the sum of angles on a straight - line (in this case, considering the angles around the point where the lines intersect) is \(180^{\circ}\)).

Step2: Simplify the equation

First, simplify the left - hand side of the equation: \(16x+116 = 180\).
Then, subtract \(116\) from both sides: \(16x=180 - 116\).
So, \(16x = 64\).

Step3: Solve for \(x\)

Divide both sides of the equation \(16x = 64\) by \(16\).
We get \(x=\frac{64}{16}\).

Answer:

\(x = 4\)