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What Examples Illustrate the Central Angle and Inscribed Angle Theorems?

Understanding Central Angles and Inscribed Angles

Let’s explore two cool ideas about circles: central angles and inscribed angles!

1. Central Angle Theorem

Imagine you have a circle. If you draw a central angle that measures 50 degrees, this angle is at the center of the circle.

What's cool is that the part of the circle that this angle "opens up" to, called the arc, also measures 50 degrees!

So, whenever you have a central angle, the arc it touches is the same measure as that angle.

2. Inscribed Angle Theorem

Now, let’s talk about inscribed angles. These angles are found inside the circle, touching the same arc.

If you draw an inscribed angle that looks at the same arc as our 50-degree central angle, it will be much smaller.

In fact, this inscribed angle is only half of the central angle. So, in our example, the inscribed angle would measure 25 degrees.


These ideas are super helpful when you’re solving problems about angles and arcs in circles!

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What Examples Illustrate the Central Angle and Inscribed Angle Theorems?

Understanding Central Angles and Inscribed Angles

Let’s explore two cool ideas about circles: central angles and inscribed angles!

1. Central Angle Theorem

Imagine you have a circle. If you draw a central angle that measures 50 degrees, this angle is at the center of the circle.

What's cool is that the part of the circle that this angle "opens up" to, called the arc, also measures 50 degrees!

So, whenever you have a central angle, the arc it touches is the same measure as that angle.

2. Inscribed Angle Theorem

Now, let’s talk about inscribed angles. These angles are found inside the circle, touching the same arc.

If you draw an inscribed angle that looks at the same arc as our 50-degree central angle, it will be much smaller.

In fact, this inscribed angle is only half of the central angle. So, in our example, the inscribed angle would measure 25 degrees.


These ideas are super helpful when you’re solving problems about angles and arcs in circles!

Related articles