# In triangle ABC, angle C = 90, angle A = 70, CD-bisector. find the corners of the triangle BCD.

March 24, 2021 | education

| 1. Find the degree measure of the angle B in the triangle ABC:

angle A + angle B + angle C = 180 degrees (according to the theorem on the sum of the angles of a triangle);

70 + angle B + 90 = 180;

angle B = 180 – 160;

angle B = 20 degrees.

2. Since CD is a bisector, it divides the angle C into two equal triangles:

angle ACD = angle DCB = angle C / 2 = 90/2 = 45 (degrees).

3. In triangle BCD: angle DCB = 45 degrees, angle DCB (angle B) = 20 degrees.

By the theorem on the sum of the angles of a triangle:

DCB angle + DVS angle + CDB angle = 180 degrees;

45 + 20 + CDB angle = 180;

angle CDB = 180 – 65;

angle CDB = 115 degrees.

Answer: DCB angle = 45 degrees, CDB angle = 115 degrees, DWS angle = 20 degrees.

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