In a right-angled triangle, the angle between the height and the bisector drawn from the vertex

In a right-angled triangle, the angle between the height and the bisector drawn from the vertex of the right angle is 40o. Find the larger angle of the given triangle.

1. When constructing the bisector and the height, we got a triangle with two known angles. An angle of 40 ° by condition and an angle of 90 ° formed by the height.

2. Calculate the third angle in the triangle. It is equal to 180 ° – 40 ° – 90 ° = 60 °.

3. Find the adjacent angle to the one found in step 2. It is equal to 180 ° – 60 ° = 120 °

4. Now we have another triangle, which has two known angles: one angle equal to 45 °, formed by the bisector of the 90 ° angle, and the found angle 120 °.

5. Let’s calculate the third angle in the triangle. It is equal to 180 ° – 45 ° – 120 ° = 15 °.

6. The found angle is the angle of the original right-angled triangle.

7. Therefore, we find the third corner of the original right-angled triangle.

It is equal to 180 ° – 15 ° – 90 ° = 75 °.

Answer: 75 °