Answer:
x = 80°
y = 50°
Step-by-step explanation:
the legs of the inner triangle (tangent to O, and O to point with y angle) are equal because both are the radius of the circle.
that makes the inner triangle an isoceles triangle with both angles on the baseline (tangent to point with y angle) being equal.
the angle of the tangent to the leg "tangent to O" is per definition a right angle (90°). otherwise it would not be a tangent.
one post of the right angle is 40°, so the other part (the triangle inner angle at the tangent point) is then 90-40 = 50°.
since both leg angles must be equal (as described above), y = 50° too.
and as the sum of all angles in a triangle must be 180°, that gives us for x
180 = 50 + 50 + x
x = 180 - 50 - 50 = 80°
