Final answer:
Angle BAD in the convex quadrilateral ABCD, where CA, CB, CD, and BD are all equal, is 90°, as it is the sum of two base angles from two isosceles triangles formed within the quadrilateral.
Step-by-step explanation:
The student's question seeks to find the measure of angle ∠BAD in a convex quadrilateral ABCD with the given property that lines CA, CB, CD, and BD are all equal in length. From these properties, we can discern that triangles BCA, BCD and BDA are all isosceles triangles with two sides equal. Since the sum of angles in any triangle is 180°, and the base angles in an isosceles triangle are equal, we can establish that each of these triangles have base angles of 45° and a vertex angle of 90°. Therefore, angle ∠BAD is the sum of two base angles, one from triangle BCA and one from triangle BDA, both of which are 45°. The sum is 45° + 45° = 90°.