In triangle abc, angle A is equal to 44 angle C 62. on the continuation of side AB

In triangle abc, angle A is equal to 44 angle C 62. on the continuation of side AB, the segment BD = BC is laid down, find the angle D triangle BCD.

By the property of an isosceles triangle:

The angles at the base of an isosceles triangle are equal.

It can be seen from the figure that the segment DC is our base of the triangle BDC. Therefore, we can say that the angle ВСD is equal to the angle ВDC according to the property of an isosceles triangle.

angle ВDС = (180 ° – angle DВС) / 2;

It can be seen from the figure that the DBC angle is equal to the ABC angle.

angle ABC = 180 ° – (angle BAC + angle ACB).

Substitute the values and find the unknowns:

angle ABC = 180 ° – (44 ° + 62 °) = 74 °;

angle ВDC = (180 ° – 74 °) / 2 = 53 °;

Answer: angle ВDC = 53 °.