In triangle ABC AD – bisector, angle C = 72 degrees, angle CAD = 13 degrees. Find corner B.

According to the theorem on the sum of the angles of a triangle: the sum of the angles of a triangle is 180 °. I.e:
angle A + angle B + angle C = 180 °.
Therefore: angle B = 180 ° – angle A – angle C.
It is necessary to find the angle A.
Angle A consists of two angles CAD and DAB, that is, Angle A = Angle CAD + Angle DAB.
To determine the DAB angle, we will use the property of the angle bisector: the angle bisector is a ray that emanates from its vertex, passes between its sides and divides this angle in half.
Therefore: CAD angle = DAB angle = 13 °.
Hence: angle A = 13 ° + 13 ° = 26 °.
We calculate the value of the angle B:
angle B = 180 ° – 26 ° – 72 ° = 82 °.

Answer: angle B = 82 °.

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