# Find the angles of a convex triangle if each of its angles is equal to: a) 144 °; b) 150 °; c) 170 °; d) 171 °

By hypothesis, all angles of a convex polygon are equal, then this polygon is regular.
The degree measure of the angle of a regular polygon is calculated by the formula:
α = (n – 2) / n * 180 °,
where α is the angle of a regular polygon, n is the number of sides of a regular polygon.
Then:
(180 ° * (n – 2)) / n = α;
(180 ° * n – 180 ° * 2) / n = α;
(180 ° * n – 360 °) / n = α;
180 ° * n – 360 ° = α * n (proportional);
180 ° * n – α * n = 360 °;
n * (180 ° – α) = 360 °;
n = 360 ° / (180 ° – α) (proportional).
a) α = 144 °.
n = 360 ° / (180 ° – 144 °) = 360 ° / 36 ° = 10.
b) α = 150 °.
n = 360 ° / (180 ° – 150 °) = 360 ° / 30 ° = 12.
c) α = 170 °.
n = 360 ° / (180 ° – 170 °) = 360 ° / 10 ° = 36.
d) α = 171 °.
n = 360 ° / (180 ° – 171 °) = 360 ° / 9 ° = 40.
Answer: a) n = 10; b) n = 12; c) n = 36; d) n = 40. One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.