Question

find the values of x and y.
42°
(16x)°
(5y - 7)°
x =
y =

Explanation:

Step1: Use angle - sum property for perpendicular lines

Since $\angle AFC = 90^{\circ}$, and $\angle AFB=42^{\circ}$, $\angle BFC = 90^{\circ}-42^{\circ}=48^{\circ}$. Also, $\angle BFC=(16x)^{\circ}$, so we set up the equation $16x = 48$.

Step2: Solve for x

Dividing both sides of the equation $16x = 48$ by 16, we get $x=\frac{48}{16}=3$.

Step3: Use angle - sum property for perpendicular lines again

Since $\angle EFD = 90^{\circ}$, and $\angle EFD=(5y - 7)^{\circ}$, we set up the equation $5y-7 = 90$.

Step4: Solve for y

Add 7 to both sides of the equation $5y-7 = 90$: $5y=90 + 7=97$. Then divide both sides by 5, we get $y=\frac{97}{5}=19.4$.

Answer:

$x = 3$
$y = 19.4$