In a right-angled triangle ABC, the bisector CD is drawn from the vertex of the right angle.

In a right-angled triangle ABC, the bisector CD is drawn from the vertex of the right angle. Find the ACD angle if the angle is B = 32 degrees.

Consider a triangle ABC, in which we know two angles:

angle ACB – straight = 90 °;

angle ABC = 32 °;

Since the sum of all the angles of a triangle is 180 °, we will find the third angle in this triangle:

angle BAC = 180 ° – 90 ° – 32 ° = 58 °;

Consider triangle ADC, in which we know two angles:

angle ADC – straight line = 90 ° (since CD is the height drawn to the hypotenuse);

angle DAC = angle BAC = 58 °;

Since the sum of all the angles of a triangle is 180 °, we will find the third angle in this triangle:

angle DCA = 180 ° – 90 ° – 58 ° = 32 °.

Answer: 32 °.