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Isosceles With Letters

Part of the Circles section of Coddy's Geometry journey. Lesson 24 of 62.

When a base angle carries a letter, the isosceles rule gives an equation: two equal base angles and the apex add to 180°. The board writes it with your labels as soon as you name the rule.

$Triangle OAB in circle O: apex 120 degrees, base angle x plus 10$

Here the apex is 120° and a base angle is (x + 10)°. Both base angles are x + 10, so 2(x + 10) + 120 = 180. Then 2(x + 10) = 60, x + 10 = 30 and x = 20. Check: the base angles are 30° each, and 30 + 30 + 120 = 180.

Challenge

A and B are on circle O. Tap angles of triangle OAB, pick the rule that connects them, and solve the equation the board writes for x.

Then press Check.

Try it yourself

$Use the figure to find x$

Use the figure to find x

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 CenterIsosceles With LettersRecap: 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