Polygon Angles with x

Part of the Polygons & Quadrilaterals section of Coddy's Geometry journey. Lesson 4 of 61.

When the angles carry a letter, Angles in a polygon gives an equation instead of a number. A square in a corner counts as 90° in that equation, like any other label.

$Quadrilateral with angles x, 2x, 120 degrees and a right angle$

Here the four angles add up to 360: x + 2x + 120 + 90 = 360. Collect the terms to get 3x + 210 = 360, so 3x = 150 and x = 50. The angles are 50° and 100°, and 50 + 100 + 120 + 90 = 360.

On the board, tap the angles, pick the rule, and the board writes the equation as your own line. Then solve it with the moves.

Challenge

Quadrilateral ABCD has one right angle and three labelled angles. Tap the four angles, pick the rule that connects them, and solve the equation the board writes for x.

Then press Check.

Try it yourself

$Use the figure to find x$