The height of an acute-angled triangle of triangle ABC forms 18 degrees and 46 degrees with sides

The height of an acute-angled triangle of triangle ABC forms 18 degrees and 46 degrees with sides entering from the same vertex. Find the angles of triangle ABC

1) BD – the height of the triangle, omitted from point B.
Find the angle ABC:
∠ ABC = ∠ ABD + ∠ CBD = 18 + 46 = 64 °.
2) Find the angles BAD and BCD.
Triangles BDA and BDC are rectangular.
By Corollary 1 of the theorem on the sum of angles in a triangle, the sum of acute angles in them is 90 °.
∠ DBC + ∠ BCD = 90 °;
∠ BCD = 90 – 46 = 44 °;
∠ ABD + ∠ BAD = 90 °;
∠ BAD = 90 – 18 = 72 °;
3) Let’s check by the theorem on the sum of angles in a triangle:
∠ BAC + ∠ ABC + ∠ BCA = 180 °;
72 + 44 + 64 = 180 °.