Find the angles of a convex pentagon if their degree measures are in the ratio 1: 5: 15: 16: 17.

Decision:

SUMA = 180 ° (n – 2) = 180 ° * (5 – 2) = 440 °.

Let ∠A = x °, ∠B = 5x °, ∠C = 15x °, ∠D = 16x °, ∠E = 17x °. We have the equation:

x + 5x + 15x + 16x + 17x = 440,

54x = 440,

x = 440: 54,

x = 220/27.

Therefore, ∠A = 220/27 ° = 8 4/27 °, ∠B = 5 * 220/27 ° = 40 20/27 °, ∠C = 15 * 220/27 ° = 122 6/27 °, ∠D = 16 * 220/27 ° = 130 10/27 °, ∠E = 17 * 220/27 ° = 138 14/27 °.

Answer: 8 4/27 °, 40 20/27 °, 122 6/27 °, 130 10/27 °, 138 14/27 °.