The height of the triangle divides the angle from the vertex of which it is lowered into parts equal to 30

The height of the triangle divides the angle from the vertex of which it is lowered into parts equal to 30 and 40 degrees, respectively. Determine the measure of the smaller angle

1. A, B, C – the vertices of the triangle. ∠С = 90 °. СK – height. ∠АВК = 30 °. ∠ВСК = 40 °.

2. The total value of the angles ΔАВК, according to its properties, is 180 °. Applying this property, we calculate the degree value ∠BAK (B):

∠ВAK (A) = 180 ° – ∠AKВ – ∠AВK = 180 ° – 90 ° – 30 ° = 60 °.

3. We calculate the degree value of ∠BAC (B) of rectangular ΔВСК: ∠ВСК (С) = 180 ° – ∠СKВ – ∠ВСК = 180 ° – 90 ° – 40 ° = 50 °.

4.∠В = ∠АВК + ∠ВСК = 30 ° + 40 ° = 70 °.

The answer is ∠C = 50 ° – the smaller angle of the triangle.