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Exterior Angles Exploration

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Exterior Angles Exploration

A supermarket is planning floor decals shaped like polygons. Help Rawiri check the turning angles so each design closes neatly. For a convex polygon, one exterior angle at each vertex makes a full turn of 360°. At each vertex, the interior and exterior angles add to 180°. Show your working where you can.

Explore the turns

Use the angle facts to investigate how polygon corners fit together.

1.At one corner of a decal, the interior angle is 127°. What is the exterior angle at that corner? Explain the calculation briefly.

2.Rawiri measures three exterior angles of a triangular decal as 105° and 130° for two corners. Find the third exterior angle.

3.Choose the correct pair of statements about a convex polygon's exterior angles.

Their sum is 180°, and regular polygons have different exterior angles.
Their sum is 360°, and a regular polygon has equal exterior angles.
Their sum depends on the number of sides, and each is equal to 90°.
Their sum is 360°, and each exterior angle equals its interior angle.

4.A regular hexagonal special display has six equal exterior angles. Calculate the size of each exterior angle.

Solve the display-design clues

Use the full-turn rule to check each design. Exterior angles are measured as the polygon is traced in the same direction.

5.A regular polygon has exterior angles of 40° each. How many sides does it have? Show the division you use.

6.A five-sided decal has exterior angles 72°, 68°, 95° and 55° at four vertices. Find the missing exterior angle.

7.A quadrilateral design has exterior angles 85°, 95°, 110° and x°. Find x, then calculate the interior angle at the corner with exterior angle x.

8.Hemi claims, “A polygon with more sides always has a larger sum of exterior angles.” Is the claim correct? Use the triangle and hexagon to support your answer.

9.A convex polygon walk starts facing east. At each vertex, the walker turns through that vertex's exterior angle and follows the next side. After going all the way around, how many degrees has the walker turned altogether, and why?

10.A regular polygon has 12 sides. Work out its exterior angle and its interior angle at each vertex.