In triangle ABC, angle A = 32 °, angle C = 74 °. On the continuation of the AB side, the segment BD = BC

In triangle ABC, angle A = 32 °, angle C = 74 °. On the continuation of the AB side, the segment BD = BC is postponed. Find the angle D of triangle BCD.

In a triangle, the sum of the angles is 180 °. We know two angles of the triangle ABC. Find corner B.

180 – (32 + 74) = 180 – 106 = 74 °.

ABD is a flat angle of 180 °. The sum of the adjacent angles ABC and CBD forms the extended angle ABD. From here we will find the CBD angle. A ___ B / __ D

180 – 74 = 106 °.

Consider a triangle CBD.

Since BC = BD, it is an isosceles triangle with equal angles at the base of DC.

180 – 106 = 74 ° – the sum of two angles at the base.

74: 2 = 37 ° is the desired angle D.