In triangle ABC, angle A = 40 degrees, angle C = 80 degrees, and the height AD is drawn. Find the corners of triangle ADB.

In triangle ABC:

Angle A = 40 °;
Angle C = 80 °;
The height АD is drawn.
Find the corners of the triangle ADB.

Decision.

1) Height is perpendicular to BC. This means that the angle BDA = angle ADC = 90 °.

2) Since the triangle ADC is rectangular and the angle ACD = 80 ° is known, then we can find the angle CAD.

Angle СAD = 180 ° – 90 ° – 80 ° = 90 ° – 80 ° = 10 °.

3) Since the angle CAB = 40 ° and the angle CD = 10 °, then we find the angle DAB.

DAB angle = 40 ° – 10 ° = 30 °.

3) Since the triangle ADB is rectangular and the angle DAB = 30 ° is known, then we can find the angle ABD.

Angle ABD = 180 ° – 30 ° – 90 ° = 150 ° – 90 ° = 60 °.

Answer: The angles of triangle ADB are 90 °, 60 ° and 30 °.