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.