The heights of the triangle, intersecting at point H, form six angles with an apex at point H.

The heights of the triangle, intersecting at point H, form six angles with an apex at point H. Determine these angles if the angles of this triangle are 50 °, 60 °, 70 °

In a right-angled triangle ABB1, we define the angle ABB1. ABB1 = 180 – 90 – 50 = 40.

In a right-angled triangle BHC1, we define the angle C1HB = 180 – 90 – 40 = 50.

Then the angle СНВ1 = С1НВ = 50 as vertical angles.

In a right-angled triangle ВСВ1, define the angle CBВ1. СBВ1 = 180 – 90 – 70 = 20.

In a right-angled triangle BHA1, we define the angle A1HB = 180 – 90 – 20 = 70.

Then the angle АНВ1 = А1НВ 70 = as vertical angles.

ВНВ1 – expanded angle, which is equal to 180, then the angle СНА1 = 180 – СНВ1 – ВНА1 = 180 – 50 – 70 = 60.

Then the angle CHA1 = ANC1 = 60 = as vertical angles.

Answer: The angles by which the height triangle is divided are: 50, 60, 70, 50, 60, 70.