The two angles of the triangle are 70 and 80 degrees, at what angle each side is visible from the center of the inscribed circle.

1. The sum of the angles of a triangle is 180 °:

∠A = α = 70 °;
∠B = β = 80 °;
∠C = γ = 180 ° – (α + β) = 180 ° – (70 ° + 80 °) = 180 ° – 150 ° = 30 °.
2. The radii drawn to the tangency points are perpendicular to the tangent:

∠AOC1 = ∠AOB1 = 90 ° – α / 2 = 90 ° – 70 ° / 2 = 90 ° – 35 ° = 55 °;
∠BOC1 = ∠BOA1 = 90 ° – β / 2 = 90 ° – 80 ° / 2 = 90 ° – 40 ° = 50 °;
∠COA1 = ∠COB1 = 90 ° – γ / 2 = 90 ° – 30 ° / 2 = 90 ° – 15 ° = 75 °.
3. The sides of the triangle ABC are visible respectively from the center of the circle at angles:

side AB;
∠AOB = ∠AOC1 + ∠BOC1 = 55 ° + 50 ° = 105 °;
side BC;
∠BOC = ∠BOA1 + ∠COA1 = 50 ° + 75 ° = 125 °;
AC side;
∠AOC = ∠COB1 + ∠AOB1 = 75 ° + 55 ° = 130 °.
Answer: 105 °; 125 °; 130 °.