Question

find the value of x.

x =

Explanation:

Step1: Recall the sum of angles around a point

The sum of angles around point \( F \) is \( 360^{\circ} \). Since \( \angle BFD = 90^{\circ} \), we can write the equation: \( 16x+90 + 26=180 \) (because \( \angle AFE=\angle CFD \) (vertical angles), and we consider the straight - line \( AFD \) which is \( 180^{\circ} \)).

Step2: Simplify the equation

Simplify \( 16x+90 + 26=180 \) to \( 16x+116 = 180 \).
Subtract \( 116 \) from both sides: \( 16x=180 - 116 \).
So, \( 16x = 64 \).

Step3: Solve for \( x \)

Divide both sides by \( 16 \): \( x=\frac{64}{16} \).

Answer:

\( 4 \)