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 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

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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