https://file.aiquickdraw.com/mathbot/file/1726095602353v5lbh6bw.jpg

The problem in the image involves a circle with several lines drawn from its center and some chords. We are given an angle inside the circle (58°), and our task is to find the shaded angle near the circumference of the circle.

To solve this, we can apply properties of angles in a circle:

1. The 58° angle is subtended by an arc of the circle, and it is an *angle at the center* of the circle.
2. The shaded angle is an *inscribed angle*, which subtends the same arc.

### Key Property:
- **An angle at the center of a circle is twice the angle at the circumference subtended by the same arc**. This property can be written as:
  \[
  \theta_{\text{center}} = 2 \times \theta_{\text{circumference}}
  \]
  where \(\theta_{\text{center}}\) is the angle at the center (58°), and \(\theta_{\text{circumference}}\) is the shaded angle.

### Calculation:
Let the shaded angle be \(x\). From the property above, we have:
\[
58^\circ = 2x
\]
Dividing both sides by 2:
\[
x = \frac{58^\circ}{2} = 29^\circ
\]

Thus, the shaded angle is **29°**.

Would you like more details, or have any further questions?

Here are some related questions to extend this topic:
1. What is the relationship between the angle at the center and angles subtended by the same arc on the circumference?
2. How can you find the angle subtended by a semicircle?
3. What is the general property of opposite angles in a cyclic quadrilateral?
4. How do you calculate the length of a chord using the angles subtended by it?
5. What is the difference between central and inscribed angles in a circle?

**Tip:** Always remember that an angle subtended by a diameter at the circumference of a circle is a right angle (90°).

Find the shaded angle in a circle, where a central angle measures 58°.

This problem involves calculating the shaded angle subtended by the same arc as a 58° central angle in a circle. Learn how to apply the Angle at the Center Theorem to find that the shaded angle is 29°. Suitable for students in Grades 9-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation