Answer
x = 4 units
y = 30°
Step-by-step explanation
The secant-secant product theorem explains that If two secant segments are drawn to a circle from an exterior point, then the product of the measures of one secant segment and its external secant segment is equal to the product of the measures of the other secant segment and its external secant segment.
In mathematical terms, using the diagram given,
4 × (4 + x) = 2 × (2 + 8)
16 + 4x = 2 × 16
16 + 4x = 32
4x = 32 - 16
4x = 16
Divide both sides by 4
(4x/4) = (16/4)
x = 4 units.
Then the secant angle theorem explains that
25° = (80° - y)/2
Cross multiply
2 × 25° = 80° - y
50° = 80° - y
y = 80° - 50°
y = 30°
Hope this Helps!!!