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This diagram shows a circle with an inscribed angle of \( 29^\circ \), and an external angle labeled \( d^\circ \), formed by the tangent line to the circle.

### To find \( d^\circ \):

In a circle, the measure of the external angle \( d \) is related to the measure of the inscribed angle by the fact that the external angle is equal to the supplementary angle of the inscribed angle. 

For this configuration:

\[
d = 180^\circ - 29^\circ = 151^\circ
\]

Thus, the value of \( d \) is:

\[
d = 151^\circ
\]

Would you like more details on the reasoning, or do you have any other questions?

### Related Questions:
1. What is the relationship between inscribed angles and their intercepted arcs?
2. How is the measure of an angle formed by a tangent and a chord calculated?
3. Can you explain the properties of supplementary angles?
4. How does the inscribed angle theorem apply to circles?
5. What is the difference between a tangent and a secant in a circle?

**Tip**: Always look for relationships between angles in a circle, such as between inscribed angles and arcs, or between angles formed by tangents and chords.

What is the value of the external angle d in the given circle diagram where the inscribed angle is 29°?

Learn how to calculate the external angle formed by a tangent to a circle given an inscribed angle of 29°. Using the inscribed angle theorem and supplementary angles, this problem demonstrates key geometry concepts, suitable for high school students in Grades 9-12.

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