Question

Find the angle of CD. Round to the nearest tenth. 12.7 cm 45.5° 9/06 cm mCD= [?]°​

Answer 1

Using the information in the diagram, the measure of $\overset{\LARGE\frown}{CD}$ is 89.0°

Calculating the angle subtended by an arc

From the question, we are to determine the measure of $\overset{\LARGE\frown}{CD}$

Consider the right triangle

The measure of $\overset{\LARGE\frown}{CD}$ is twice the measure of the unknown angle

Let the unknown angle in the right triangle be x

∴ The measure of $\overset{\LARGE\frown}{CD}$ = 2x

Then,

x + 90° + 45.5° = 180° (Sum of angles in a triangle)

x = 180° - 90° - 45.5°

x = 44.5°

Thus,

The measure of $\overset{\LARGE\frown}{CD}$ = 2×44.5°

The measure of $\overset{\LARGE\frown}{CD}$ = 89°

Hence, the measure of $\overset{\LARGE\frown}{CD}$ is 89.0°

Learn more on Calculating the angle subtended by an arc here: https://brainly.com/question/1213527

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