Let's focus on **Question 12** from the image. The problem is as follows:

### Question 12:
In the figure, ∠BOD = 120°. Find the measure of ∠ABC.

**Solution:**

Given that ∠BOD = 120°, we want to find the measure of ∠ABC.

1. **Central Angle and Inscribed Angle Relationship:**
   - The central angle ∠BOD subtends the arc \(BD\) on the circle.
   - An inscribed angle that subtends the same arc \(BD\) will be half of the central angle.

   Therefore, 
   \[
   \angle ABC = \frac{1}{2} \times \angle BOD
   \]

2. **Substitute the value of ∠BOD:**
   \[
   \angle ABC = \frac{1}{2} \times 120^\circ = 60^\circ
   \]

**Answer:**
The measure of \(\angle ABC\) is \(60^\circ\).

Would you like more details on this, or do you have any other questions? Here are some related questions to explore:

1. How do you find the measure of an inscribed angle if the central angle is unknown?
2. What is the relationship between an inscribed angle and its opposite arc?
3. How does the angle subtended by a diameter at the circumference behave?
4. What is the measure of an angle in a semicircle?
5. How can the angle sum property of a triangle be used in circle geometry?

**Tip:** When dealing with circles, always remember the relationships between central angles, inscribed angles, and the arcs they subtend. This can simplify solving many problems.

Learn how to find the measure of angle ABC in circle geometry with a detailed step-by-step solution. Given that angle BOD is 120°, discover how to use central and inscribed angle relationships to determine angle ABC as 60°. Ideal for high school students studying circle theorems.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation