The angle between the bisector and the median of a right-angled triangle drawn

The angle between the bisector and the median of a right-angled triangle drawn from the apex of the right angle is 21 degrees. Find the smaller angle of this triangle.

Let us denote the triangle ABC given by the condition, angle C – a straight line. CD is the bisector of the right angle, CM is the median drawn from the right angle to the hypotenuse.
Consider a triangle AMC, it is isosceles, according to the property of the median in a right-angled triangle (CM – half of the hypotenuse, CM = AM).
∠CAM = ∠ACM (angles at the base of an isosceles triangle).
∠CAM = ∠ACM = ∠ACD – ∠MCD = 45 ° – 21 ° = 24 ° is the angle at the vertex A in the right-angled triangle ABC.
∠B = 90 ° – 24 ° = 66 °.
We get that the smaller angle is angle A.
Answer: Angle A is 24 ° and this is the smaller angle.