Find the angles of triangle ABD in triangle ABC with right angle C, if angle CBD is 20 degrees.

1. We calculate the degree measure ∠АВD, taking into account that the bisector ВD divides ∠В into two equal angles:

∠АВD = ∠СВD = 20 °.

2. ∠В = ∠АВD + ∠СВD = 20 ° + 20 ° = 40 °.

3. We calculate the degree measure ∠A, taking into account that the total value of the angles of the triangle ABC is 180:

∠ВАD = 180 – ∠В – ∠С = 180 ° – 40 ° – 90 ° = 50 °.

4. Calculate the degree measure ∠ADB:

∠ADB = 180 – ∠ABD – ∠A = 180 ° – 20 ° – 50 ° = 110 °.

Answer: the angles of the triangle ABD – ∠ADB = 110 °, ∠ВАD = 50 °, ∠ABD = ∠СВD = 20 °.