To what extent can the flat angle of a trihedral angle change if the two remaining ones are respectively equal to 130 and 160?

Let the value of the unknown trihedral angle be X0.

By the property of a polyhedral angle, the sum of the flat angles of a trihedral angle is less than 3600, and each flat angle is less than the sum of its two other flat angles.

Let the third angle be equal to X0.

Then:

X + 130 + 160 <3600.

X + 130> 160.

Let us solve the system of two inequalities.

X <360 – 130 – 160.

X <70.

X> 160 – 130.

X> 30.

30 <X <70.

Answer: The plane angle varies within 30 <X <70.