Using the Same Arc

Part of the Circles section of Coddy's Geometry journey. Lesson 38 of 62.

To use the rule, find the chord both angles stand on, then check that the two vertices are on the same side of it. If they are, the angles are equal.

$Inscribed angles at P and Q on the chord AB, both 47 degrees$

Here ∠APB and ∠AQB both open onto the arc AB below, and P and Q are both above the chord. So ∠AQB = ∠APB = 47°. On the board, tap the unknown angle and pick Angles on the same arc.

Challenge

P and Q are on circle O, on the same side of the chord AB. Find ∠AQB, 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

2Circumference

Around the Circle Using the Diameter Radius From Circumference Circumference With Letters Recap: Circumference

5Radii Make Isosceles

Two Radii, One Triangle Base Angles From the Center The Angle at the Center Isosceles With Letters Recap: Radii and Triangles

8Angles on the Same Arc

Same Arc, Same AngleUsing the Same ArcSpot 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