Let's analyze and answer the questions based on the provided image:

Question 11

Which one of the following angles is inscribed on a major arc?

• (a) Acute angle
• (b) Right angle
• (c) Obtuse angle
• (d) Reflex angle

Explanation:

An angle inscribed on a major arc is typically larger than 180°, making it a reflex angle.

Answer: (d) Reflex angle

Question 12

What is the value of $x$?

• (a) 30°
• (b) 35°
• (c) 60°
• (d) 70°

Explanation:

From the diagram, it looks like there’s a central angle (labeled as 70°) and an inscribed angle (labeled as $x$) that subtends the same arc. In a circle, the inscribed angle is half of the central angle subtending the same arc.

Since the central angle is 70°: $x = \frac{70^\circ}{2} = 35^\circ$

Answer: (b) 35°

Question 13

What is the value of $y$?

• (a) 60°
• (b) 80°
• (c) 130°
• (d) 140°

Explanation:

The angle $y$ appears to be opposite the central angle and is formed by two intersecting chords. It should satisfy the circle angle properties or be determined by the inscribed angles.

However, without additional information, we can make an educated guess by considering that in a common setup, angles like $y$ tend to be supplementary to other angles in similar diagrams. Thus, the answer could reasonably be estimated if assuming symmetry, or additional circle theorem logic might imply that:

Answer: (b) 80°

Would you like further detailed explanations or help with related questions?

Related Questions:

1. What is a reflex angle, and why is it greater than 180°?
2. How do you calculate inscribed angles based on central angles?
3. What is the difference between inscribed angles and central angles in a circle?
4. Can an obtuse angle ever be inscribed on a major arc?
5. How does the supplementary angle rule apply to angles in circles?

Tip:

Remember, the inscribed angle theorem states that an angle inscribed in a circle is half the measure of the central angle subtending the same arc. This is a fundamental property used frequently in circle geometry problems.