Inscribed With Letters

Part of the Circles section of Coddy's Geometry journey. Lesson 30 of 62.

With letters in the labels, the inscribed angle rule becomes an equation: twice the inscribed angle equals the central angle. Write the 2 around the whole inscribed label.

$Central angle 2x plus 10 and inscribed angle 40 degrees on the same arc$

Here the central angle is (2x + 10)° and the inscribed angle is 40°. The rule gives 2 × 40 = 2x + 10, so 80 = 2x + 10, 2x = 70 and x = 35. Check: the central angle is 80°, twice 40°.

Challenge

∠APB is inscribed in circle O and ∠AOB is the central angle on the same arc. Tap the two angles, pick the rule that connects them, and solve the equation the board writes for x.

Then press Check.

Try it yourself

$Use the figure to find x$