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Interior Angles Exploration
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Interior Angles Exploration
You are helping plan a geometric pavilion. Use interior-angle sums and ratios to check that its polygon designs fit together. Show your calculations and include ° in angle answers.
Angle-sum toolkit
A polygon with n sides can be split into (n − 2) triangles. Its interior-angle sum is (n − 2) × 180°. A ratio such as 2:3:4 means the angles are 2x, 3x and 4x.
1.One angle of a triangular panel is 48° and another is 67°. Find the third angle.
2.A four-sided floor tile is a quadrilateral. What is the sum of its interior angles?
- 180°
- 270°
- 360°
- 540°
3.A quadrilateral has angles 82°, 96°, 105° and x°. Calculate x.
4.The interior angles of a quadrilateral are in the ratio 2:3:4:3. Find all four angles.
5.A hexagon can be divided into four triangles by drawing diagonals from one vertex, so its interior angles sum to 720°. Is this statement true or false? Explain briefly.
6.A pentagonal roof has interior angles in the ratio 3:4:4:5:4. Work out the size of each angle.
7.A designer claims that a regular hexagonal feature has interior angles of 120° each and an interior-angle sum of 600°. What is wrong with the claim?
8.Complete the rule for an n-sided polygon: number of triangles from one vertex = ; interior-angle sum = .
9.An octagon has interior angles in the ratio 5:5:6:6:6:6:7:7. Calculate the value of one ratio part and the size of each of the eight angles.
10.In two or three sentences, explain how you would find the angles of any polygon when their ratio is given.
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