Answer:
Therefore, the angle ∠CDA is 58°.
Explanation:
∠CDA = 58°
In the given figure, let's consider the angle ∠CDA as x.
Since AB is the diameter of the circle, we know that the angle subtended by any diameter at any point on the circumference is always 90°. Therefore, ∠CAB = 90°.
In triangle CAD, the sum of angles is 180°. So, we have:
∠CAD + ∠CDA + ∠CAB = 180°
Substituting the known values:
32° + x + 90° = 180°
Combining like terms:
x + 122° = 180°
Subtracting 122° from both sides:
x = 180° - 122°
x = 58°