The angles of a convex quadrangle are 5: 6: 9: 10. Find the degree measure of the smaller angle of this quadrilateral.

In order to find the angles of a quadrilateral, we start by looking at and analyzing a given condition.

We know that the angles of a convex quadrilateral are 5: 6: 9: 10. To solve, we compose and solve the equation. We know that the sum of the angles of a convex quadrilateral is 360 °.

Let’s enter a coefficient of similarity k and designate the angles as 5k, 6k, 9k and 10k.

We write the equation:

5k + 6k + 9k + 10k = 360;

k (5 + 6 + 9 + 10) = 360;

30k = 360;

k = 12.

The angles are equal: 5 * 12 = 60 °; 6 * 12 = 72 °; 9 * 12 = 108 °, 10 * 12 = 120 °.