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 °.
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