points a, b, c, and d lie on circle m. line segment bd is a diameter. the measure of arc cd equals the…

Explanation:

Step1: Recall circle - angle relationship

A diameter subtends a right - angle at the circumference. So, $\angle BAD = 90^{\circ}$ since $BD$ is a diameter.

Step2: Use arc - angle relationship

The measure of an inscribed angle is half the measure of its intercepted arc. Let the measure of arc $CD$ and arc $DA$ be $x$. The sum of arc $CD$ and arc $DA$ is a semi - circle (because $BD$ is a diameter), so $x + x=180^{\circ}$, then $2x = 180^{\circ}$, and $x = 90^{\circ}$.

Step3: Calculate $\angle ADM$

The measure of inscribed angle $\angle ADM$ is half the measure of arc $AM$. Since arc $DA = 90^{\circ}$ and $M$ is the center of the circle, the measure of $\angle ADM=\frac{1}{2}\times90^{\circ}=45^{\circ}$.

Answer:

$45.0^{\circ}$