In a right-angled triangle, the angle between the height and the bisector drawn from

In a right-angled triangle, the angle between the height and the bisector drawn from the top of the right angle is 14 degrees. Find the degree measure of the smaller angle of this triangle.

1. Let us introduce the designation of the vertices of the triangle by the symbols A, B, C. Angle C = 90 °. KCY angle = 14 °.

CH – height, CK – bisector. Point K is on the side AB between points H and B.

2. Angle BCK = 90 °: 2 = 45 °, since the bisector CR divides the right angle C into two equal parts.

3. Angle АСН = 45 ° – 14 ° = 31 °.

4. Angle AHC = 90 °, since CH is the height. Angle A = 180 ° – 31 ° – 90 ° = 59 °.

5. Angle B = 180 ° – 59 ° – 90 ° = 31 °.

Answer: the smaller angle of the triangle ABC is the angle B, equal to 31 °.