Answer:
see explanation
Step-by-step explanation:
(1)
x + 20 and 45 are vertically opposite angles and are congruent, so
x + 20 = 45 ( subtract 20 from both sides )
x = 25
Similarly 5y and 135 are vertically opposite angles and are congruent
5y = 135 ( divide both sides by 5 )
y = 27
(2)
x + 30 and 70 are vertically opposite angles and are congruent, then
x + 30 = 70 ( subtract 30 from both sides )
x = 40
Similarly y + 50 and 110 are vertically opposite and congruent , so
x + 50 = 110 ( subtract 50 from both sides )
x = 60
EF is tangent to the circle we'll assume; otherwise there's no progress.
Call the center C. ECD is isosceles, formed from two radii and the chord.
Angle CED is complementary to DEF
CED = 90 - 65 = 25 degrees
CDE is congruent, isosceles triangle and all that: CDE=25
That leaves DCE=180-25-25=130 degrees
That's the measure of arc DE as well:
Answer: 130 degrees, choice A
