In triangle ABC, angle A = 59 degrees, angle B = 62. From the vertices of these angles, heights are drawn

In triangle ABC, angle A = 59 degrees, angle B = 62. From the vertices of these angles, heights are drawn that intersect at point O. Find the degree measure of angle AOB

1) Triangle ABC. Angle A = 59 ° and angle B = 62 °.
2) Consider a right-angled triangle ABK with a right angle K.
Angle B = 62 °, angle K = 90 °.
Let’s find the angle AВK.
ВAK angle = 180 ° – 90 ° – 62 ° = 90 ° – 62 ° = 30 ° – 2 ° = 28 °;
3) Consider a right-angled triangle ABН with a right angle H.
Angle A = 59 °, angle H = 90 °.
Let’s find the angle AВK.
AВН angle = 180 ° – 90 ° – 59 ° = 90 ° – 59 ° = 40 ° – 9 ° = 31 °;
4) Consider the ABO triangle.
Angle AOB = 180 ° – angle AВН – angle ВAK = 180 ° – 31 ° – 28 ° = 130 ° – 1 ° – 8 ° = 130 ° – 9 ° = 121 °.
Answer: Angle AOB = 121 °.