A bisector of an acute angle is drawn in a right-angled triangle. One of the angles of the newly obtained

A bisector of an acute angle is drawn in a right-angled triangle. One of the angles of the newly obtained triangle is equal to 70 *. Find the value of the angles of the original triangle.

1. Vertices of triangle A, B, C. AK bisector. ∠АКС = 70 °. ∠АСВ = 90 °.

2. Calculate the degree measure ∠СAK of a right-angled triangle НAO:

∠СAK = 180 ° – (∠АКС + ∠АСК) = 180 ° – (70 ° + 90 °) = 20 °.

3. We calculate the value of ∠BAC:

∠BAC = 2∠СAK, since the bisector divides ∠BAC into two equal angles.

∠BAC = 2 x 20 ° = 40 °.

4. We calculate the degree measure ∠ABС:

∠ABS = 180 ° – (∠ВАС + ∠АСВ) = 180 ° – 130 ° = 50 °.

Answer: ∠ABS = 50 °, ∠BAC = 40 ° – the angles of the triangle ABC. ∠АСВ = 90 ° is given by the condition of the problem