In a right-angled triangle DCK, the outside angle at the vertex D is 153 degrees. Find the magnitude of the acute angle C.

The sum of the outer and inner angles of a triangle taken at one vertex is 180 degrees. This means that the inner angle of the triangle at the vertex D is 180 ° – 153 ° = 27 °.

In a right-angled triangle, the sum of the acute angles is 90 degrees. In our case, the acute angles of the triangle are angle D and angle C.

∠D + ∠C = 90 °;

∠C = 90 ° – ∠D;

∠C = 90 ° – 27 ° = 63 °.

Answer. ∠C = 63 °.