# Angle Properties of Circles

Hi students! Today, we will be learning about the ** angle properties of circles**. These properties are extremely helpful to help you solve questions related to circles. Without further ado, let’s begin!

This is a continuation from our previous article, ** symmetrical properties of circles.** Do click on the link to learn more if you happen to miss it!

__Angle Properties of Circles__

· __Angle at center = 2 × Angle at circumference__

· __Right angle in semicircle__

· __Angles in same segment are equal__

· __Angles in opposite segments are supplementary__

__Angle Properties of Circles__

__Angle Properties of Circles__

### 1) __Angle at center = 2 × Angle at circumference__

· **An angle at the center of a circle is twice that of any angle at the circumference subtended by the same arc, i.e. ∠FOG = 2 x ∠FMG**

### 2) __Right angle in semicircle__

· **An angle in a semicircle is always equal to 90°, i.e. XOY is a diameter, ∠XNY = 90°**

### 3) __Angles in same segment are equal__

· **Angles in the same segment are equal, i.e. ∠DJE = ∠DKE = ∠DLE**

### 4) __Angles in opposite segments are supplementary__

· **Angles in opposite segments are supplementary, i.e. ∠ZWX + ∠ZYX = 180°**

And that’s all for today, students! Math Lobby hopes that after this article, you have a clear understanding on the angular properties of circles!

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