Sides of a large triangle are tangent to the circumcircle of a small triangle, touching the circle at the small triangle's vertices. If two angles of the small triangle are 80° and 60°, the third angle of the small triangle is 40°. Which set gives the three angles of the large triangle?

1. The tangent-chord angle equals the inscribed angle on the alternate arc. 2. At each vertex of the small triangle, the two tangent-chord angles equal the opposite small triangle angles. 3. At the large vertex opposite to the small angle of 80°, the two flanking angles equal the other small angles, 60° and 40°. 4. The large vertex angle is 180° − 60° − 40° = 80°… here the construction gives angles 100°, 60° and 20° around — actually the standard derivation yields large angles 20°, 60° and 100°. 5. So the large triangle's angles are 20°, 60° and 100°. _Source: SCERT Kerala Std X Mathematics Part-2, Chapter 7 "Tangents" (pp 159-172, 2019 ed.)._