Question

determine $\angle cbd$.

Explanation:

Step1: Identify the diameter and right angle

Since \( CB \) is a diameter (as \( A \) is the center and \( C, A, B \) are colinear), \( \angle CDB \) is an inscribed angle subtended by the diameter, so \( \angle CDB = 90^\circ \) (angle in a semicircle is a right angle).

Step2: Use triangle angle sum

In \( \triangle CBD \), the sum of angles is \( 180^\circ \). We know \( \angle BCD = 43^\circ \) and \( \angle CDB = 90^\circ \). Let \( \angle CBD = x \). Then:

$$ x + 43^\circ + 90^\circ = 180^\circ $$

$$ x = 180^\circ - 43^\circ - 90^\circ $$

$$ x = 47^\circ $$

Answer:

\( \angle CBD = 47^\circ \)