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Regular Shapes Together

Part of the Polygons & Quadrilaterals section of Coddy's Geometry journey. Lesson 55 of 61.

Regular polygons fit together, and the angles where they meet come from the rules you already have. Each regular polygon brings its own angle, and a point or a corner shares the rest.

$A regular hexagon with a square on side AB; the gap at A between them is 150 degrees$

A regular hexagon and a square share the side AB. At A the hexagon's corner is 120° and the square's is 90°. Round the point A all the angles make 360°, so the gap between them is 360 - 120 - 90 = 150 degrees. Inside a polygon, a shape drawn on a side takes a part of the corner instead, and Adjacent angles add gives what is left.

Challenge

ABCDE is a regular pentagon, and ABF is an equilateral triangle drawn inside it on the side AB. Find ∠FBC, marked ?, 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 Polygons & Quadrilaterals

2Regular Polygons

Regular Polygons From an Angle to the Sides Inside a Regular Polygon Recap: Regular Polygons

5Rectangles, Rhombi, Squares

Rectangles The Diagonal of a Rectangle Rhombus Angles Squares Recap: Special Parallelograms

8Area of Parallelograms

Area of a Rectangle A Side from the Area Slide the Top Area of a Parallelogram Recap: Parallelogram Area

11Polygon Chases

Parallel Sides in a Pentagon Marks, Not Looks Pentagon with xRegular Shapes TogetherRecap: Polygon Chases