A convex polygon has three angles of 80 degrees, and the rest are 150. How many angles are in a convex polygon?

Let there be x angles in a given polygon, then (x – 3) angles of 150 degrees. Recall the formula for the sum of the angles of an x-gon: S = (x – 2) * 180.
In addition, based on the condition, the sum of the angles of our x-gon is: S = 3 * 80 + (x – 3) * 150.
We equate the obtained expressions and solve the equation:
(x – 2) * 180 = 3 * 80 + (x – 3) * 150;
180x – 360 = 240 + 150x – 450;
180x – 150x = 240 + 360 – 450;
30x = 150;
x = 150: 30 = 5.
Answer: 5 corners in a convex polygon.