In triangle ABC AC = BC, AD is the height, the angle BAD is 64 °. Find the corner C.

In triangle ABC it is known:

AC = BC;
AD – height;
Angle BAD = 64 °.
Find corner C.

1) Triangle ADB.

It is known that the angle D = 90 °, the angle A = 64 °.

Find angle B of triangle ADB.

The sum of all the angles of the triangle is.

Angle B = 180 ° – 90 ° – 64 ° = 90 ° – 64 ° = 90 ° – 60 ° – 4 ° = 30 ° – 4 ° = 26 °.

2) Triangle ABC.

Angle A = angle B = 180 ° – 2 * 26 ° = 180 ° – 52 ° = 180 ° – 50 ° – 2 ° = 130 ° – 2 ° = 128 °.