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The Angle at the Center

Part of the Circles section of Coddy's Geometry journey. Lesson 20 of 59.

It works the other way round too. If you know one base angle, you know the other, because they are equal. Take both from 180° and what is left is the angle at the center.

$Triangle OAB in circle O: base angle 50 degrees, central angle 80 degrees$

Here the base angle at A is 50°, so the one at B is 50° too. Then ∠AOB = 180° - 50° - 50° = 80°. Tap the angle at the center and pick Isosceles triangle: the board uses both base angles at once.

Challenge

A and B are on circle O, and the angle at A is marked. Find the central angle ∠AOB, then press Check.

Try it yourself

$Find the marked part of the figure$

Find the marked part of the figure

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Circles

1Parts of a Circle

Center and Radius Chords and Diameters Recap: Parts of a Circle

4Arcs and Sectors

Arc Length Area of a Sector Find the Central Angle The Missing Central Angle Recap: Arcs and Sectors

7Angles in a Semicircle

Thales' Theorem The Right Angle Inside Is That Enough?Semicircle With Letters Recap: Semicircles

10Tangents

What a Tangent Is Tangent and Radius Tangent Lengths Two Tangents From a Point Tangents With Letters Recap: Tangents

2Circumference

The Hexagon Inside Around the Circle Radius From Circumference Recap: Circumference

5Radii Make Isosceles

Two Radii, One Triangle Base Angles From the CenterThe Angle at the CenterIsosceles With Letters Recap: Radii and Triangles

8Angles on the Same Arc

Same Arc, Same Angle Using the Same Arc Spot the Bow Tie Same Arc With Letters Recap: Same Arc

11Circle Chases

Tangent Meets Chord Two Roads to One Angle Enough to Find It?Cyclic Meets Isosceles Recap: Circle Chases