Cyclic With Letters
Part of the Circles section of Coddy's Geometry journey. Lesson 45 of 62.
With letters in two opposite angles, the cyclic rule gives an equation: the two labels add to 180.
Here the angle at B is (x + 30)° and the angle at D is 110°. They are opposite, so (x + 30) + 110 = 180. Then x + 140 = 180 and x = 40. Check: 70° and 110° add to 180°.
Challenge
ABCD has all four corners on circle O. Tap two opposite angles, 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
Test yourselfThis 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 RadiusChords and DiametersAll Radii Are EqualDiameter Is Two RadiiRecap: Parts of a Circle4Arcs and Sectors
Arc LengthArea of a SectorFind the Central AngleThe Missing Central AngleRecap: Arcs and Sectors2Circumference
Around the CircleUsing the DiameterRadius From CircumferenceCircumference With LettersRecap: Circumference5Radii Make Isosceles
Two Radii, One TriangleBase Angles From the CenterThe Angle at the CenterIsosceles With LettersRecap: Radii and Triangles8Angles on the Same Arc
Same Arc, Same AngleUsing the Same ArcSpot the Bow TieSame Arc With LettersRecap: Same Arc3Area of a Circle
The Area FormulaArea From the DiameterRadius From the AreaCircumference to AreaRecap: Area of a Circle6Inscribed Angles
Meet the Inscribed AngleHalf the Central AngleTwice the Inscribed AngleThe Big ArcInscribed With LettersRecap: Inscribed Angles9Cyclic Quadrilaterals
Four Corners on a CircleOpposite Angles Add to 180Is It Cyclic?Cyclic With LettersRecap: Cyclic Quadrilaterals