Answer:
x = 1
y = 30°
Step-by-step explanation:
If two secant segments are drawn to a circle from the same external point, the product of the length of one secant segment and its external part is equal to the length to the product of the other secant segment and its external part.
Secant-secant rule:
[tex]\boxed{\bf Whole \ secant * external \ part = whole \ secant * external \ part}[/tex]
(4 + x) * 4 = (2 + 8) * 2
(4 + x) * 4 = 10* 2
[tex]\sf 4 + x = \dfrac{10*2}{4}[/tex]
4 + x = 5
x = 5 - 4
[tex]\boxed{\bf x = 1}[/tex]
11) Far arc = 80°
Near arc = y°
[tex]\sf \angle A = \dfrac{far \ arc - near \ arc}{2}\\\\\\25^\circ = \dfrac{80-y}{2}\\\\\\[/tex]
25*2 = 80 - y
50 = 80 - y
50 + y = 80
y = 80 - 50
y = 30°
