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Interior Angles Exploration

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Interior Angles Exploration

Help the design team check polygon-shaped signs and ride features. For each question, show your calculations and include the degree symbol (°) in your answers.

Angle rules

Use the polygon angle-sum rule: the sum of the interior angles of an n-sided polygon is (n − 2) × 180°.

1.At the theme park entrance, a triangular sign has angles 48° and 67°. Find its third interior angle. Show the subtraction you use.

2.A four-sided floor panel has interior angles 82°, 96° and 105°. Calculate the fourth angle. Explain which angle-sum fact you used.

3.A regular hexagonal platform has six equal interior angles. Calculate the size of each interior angle.

4.A five-sided ride badge has angles 100°, 110°, 120° and two equal angles, each labelled x°. Write an equation and solve for x.

5.Talia says, “Every quadrilateral has four right angles because its angles add to 360°.” Is her reasoning correct? Explain your answer and give one example of a quadrilateral that does not have four right angles.

6.A regular polygon at the park has an interior-angle sum of 1,080°. How many sides does it have? Show how you use the polygon angle-sum rule.

7.A regular polygon has each interior angle equal to 150°. First find each exterior angle, then determine the number of sides. Assume one interior and its adjacent exterior angle make a straight line.

8.Nikau is checking a convex octagonal sign. Seven of its interior angles are 135°, 140°, 125°, 150°, 130°, 145° and 135°. Find the eighth angle.

9.A regular polygon has 9 sides. Calculate its interior-angle sum and the size of each interior angle. State why dividing the sum by 9 is valid.

10.Design a convex polygon sign for a new theme park attraction. Choose the number of sides (at least 5), calculate its interior-angle sum, and sketch the sign with one interior angle labelled. Your chosen shape and calculation must agree.