In a convex quadrilateral ABCD, the diagonals intersect and at the point of intersection are divided into two halves

In a convex quadrilateral ABCD, the diagonals intersect and at the point of intersection are divided into two halves. Find the smaller angle of quadrilateral ABCD if angle A: angle B = 2: 3

1. The diagonals of the quadrilateral ABCD are divided by the point of intersection into equal segments. This is one of the hallmarks of a parallelogram. Consequently, the geometric figure given by the condition of the problem is a parallelogram.

2. ∠А / ∠В = 2/3. ∠B = 3∠A / 2.

3. А + ∠В = 180 ° (according to the properties of the parallelogram).

4. Substitute in this expression 3∠A / 2 instead of ∠B:

∠А + 3∠А / 2 = 180 °.

5∠A = 360 °.

∠А = 72 °.

∠B = 3∠A / 2 = 3 x 72 °: 2 = 108 °.

5. Smaller angles ∠А = ∠С = 72 °.