Question

ABCD is a square. It's diagonals AC and BD intersect each other at O . Find the measure of angle CAD and angle DBC​

Answer 1

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OK, the figure ABCD, being a square, contains four 90° Angles:, DAB, ABC, BCD and CDA. The segments AC and BD are both Angle Bisectors of those four 90°; therefore, those angles, CAD and DBC as well as the other six angles: CAB, DBA, BAC, ACB, ACD, BDC, and BDA—all eight of them, having been Bisected by the segments AC and BD, are all 45°angles. In fact, the four triangles created by Angle Bisectors AC and BD, are a special form of Isosceles triangle, known as the Equilateral triangle.

The answer to your question, therefore, is: Angles CAD and DBC are 45° angles.