The MPO triangle is the sum of the two external angles at the vertices A and O equal to 230 degrees. Find the angle P.

Let the KMO angle be the external angle at the vertex M, the RON angle – the external angle at the vertex O.
By condition: KMO angle + RON angle = 230 degrees.
1. Angle CMO and angle RMO (angle M) are adjacent angles, then:
angle KMO + angle M = 180 degrees;
angle KMO = 180 – angle M.
2. Angle RON and angle POM (angle O) are adjacent angles, then:
angle RON + angle O = 180 degrees;
angle RON = 180 – angle O.
3. Substitute the obtained values ​​into the expression specified by the condition (KMO angle + RON angle = 230 degrees):
180 – angle М + 180 – angle О = 230;
– angle М – angle О = 230 – 360;
angle M + angle O = 130 degrees.
4. By the theorem on the sum of the angles of a triangle:
angle M + angle P + angle O = 180 degrees;
130 + angle P = 180;
angle P = 180 – 130;
angle P = 50 degrees.
Answer: 50 degrees.