I'll analyze and solve each question in the image.

Question 1

It involves a triangle with a specified angle measurement at point $O$. We need to determine the measure of angle $C$ based on given information. Since the triangle is labeled with angles $40^\circ$ at point $B$ and $11^\circ$ at point $D$, we should apply the angle sum property in triangles and any additional information to find the correct answer.

Solution:

1. If we consider $\angle C$ as an external angle or use the angle properties in triangles, we can sum the given angles and solve for $\angle C$.
2. The answer is likely among the options: $10^\circ, 20^\circ, 30^\circ, 40^\circ$.

Question 2

This question gives a set of inequalities and equalities between segments $MN, EF, AB,$ and $GH$. We are asked to deduce a relationship from the given conditions.

Solution:

1. We have $MN = EF$, $EF < AB$, and $AB = GH$.
2. With $EF < AB = GH$, it implies $EF < GH$.
3. This rules out the equality options and suggests the inequality options should be evaluated.

Question 3

The problem involves a divided line $AB$ with points marked $C, D, E, F, G$, dividing it into six equal segments. We need to determine which of the given relations is incorrect.

Solution:

1. By analyzing the segment lengths, if each segment (e.g., $AC, CD, DE$) is equal, we can check each relation.
2. Relations include proportions like $\frac{CF}{FB} = \frac{1}{2}$, and others, which can be tested for accuracy based on equal segment division.

Would you like further details on each solution step-by-step?

Here are 5 questions related to this type of geometry problem-solving:

1. How do we determine the exterior angle in a triangle?
2. What are the properties of segments in proportionality?
3. How can angle sum properties assist in finding unknown angles?
4. How do inequalities among segment lengths affect geometric relationships?
5. Why is it important to verify segment divisions in line segments?

Tip: Always double-check given angle and segment relationships by applying basic geometric rules, such as angle sum properties and segment proportion tests.