Through the top of an acute angle, two straight lines are drawn perpendicular to the sides

Through the top of an acute angle, two straight lines are drawn perpendicular to the sides of the angle, prove that the sum of the obtuse angle formed by these lines and this acute angle is 180.

Angle AOB is the original acute angle.

The angle DОВ is a straight line formed as a perpendicular to the ОВ.

Angle AOC is a straight line formed as a perpendicular to OA.

Angle О1ОС – unfolded angle 180.

Angle DОС – an obtuse angle formed parallel to the sides of an acute angle.

Let us prove that the angles О1ОD and AOB are equal.

Angle DОВ = DAO + AOB = 90.

Angle О1ОА = DAO + О1ОD = 90.

Therefore, the angle О1ОD = ОАD.

Then О1ОD + DОС = AOB + DАС = 180, as required.