https://file.aiquickdraw.com/mathbot/file/1726322546218fbr1z23b.jpg

I see two circle-related geometric diagrams in the image.

### For the top diagram (marked "d" and "36"):
It seems like there is a circle with two angles labeled. The angle on the right is \(36^\circ\), and the other angle on the left is labeled \(d\). Based on the context, the two angles could be part of a cyclic quadrilateral, meaning that opposite angles sum to \(180^\circ\).

Thus:
\[
d + 36^\circ = 180^\circ
\]
Solving for \(d\):
\[
d = 180^\circ - 36^\circ = 144^\circ
\]

So, \( d = 144^\circ \).

### For the bottom diagram (marked "g" with angles \(46^\circ\) and \(h\)):
This seems to be another circle with intersecting lines inside, possibly a quadrilateral inscribed in the circle. In this case, angles opposite each other in a cyclic quadrilateral add up to \(180^\circ\).

Thus, for this diagram:
\[
h + 46^\circ = 180^\circ
\]
Solving for \(h\):
\[
h = 180^\circ - 46^\circ = 134^\circ
\]

So, \( h = 134^\circ \).

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Would you like further details or have any questions?

### Related Questions:
1. What is a cyclic quadrilateral and how do its angles behave?
2. How can you apply angle properties of circles in solving more complex geometry problems?
3. What other angle relationships exist in a circle?
4. How does the inscribed angle theorem work in circle geometry?
5. Can you apply the opposite angles rule to any other shapes in circle geometry?

### Tip:
Remember that in cyclic quadrilaterals, opposite angles always sum to \(180^\circ\), a useful property for solving many circle-based problems.

What are the values of angles 'd' and 'h' in the given cyclic quadrilateral problems?

Explore how to find unknown angles in cyclic quadrilaterals using the opposite angles theorem. This problem covers circle geometry, particularly focusing on the relationship between opposite angles in a cyclic quadrilateral. Suitable for students in Grades 9-11.

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