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Interior Angles Exploration
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Interior Angles Exploration
Solve each angle puzzle. Show your working and include degree symbols in your answers. Remember: the interior angles of a triangle add to 180°.
Plan the Pavilion
A community group is planning a small pavilion. Its roof trusses and floor tiles use triangles and polygons. Use angle facts to check that the designs fit together.
1.The roof truss is triangular. Its angles are 52°, 68° and x°. What is x?
2.A triangular brace has angles in the ratio 2:3:4. Find the size of each angle.
3.A floor tile is a quadrilateral. Three interior angles are 87°, 104° and 96°. Find the fourth angle.
4.A triangular roof brace has angles 3x°, 2x° and x°. Find x and all three angles.
5.A regular pentagonal tile has five equal interior angles. The sum of its interior angles is (5 − 2) × 180°. Calculate each interior angle.
6.The pavilion’s hexagonal feature has six sides. Calculate the sum of its interior angles using (n − 2) × 180°.
7.At a triangular joint, an exterior angle is 127°. One of the two non-adjacent interior angles is 58°. Find the other non-adjacent interior angle.
8.A triangular garden bed has angles in the ratio 5:4:3. Find the three angles and state which angle is largest.
9.A polygon in the pavilion design has an interior-angle sum of 1,080°. How many sides does it have? Show how you know.
10.A regular polygon has an interior-angle sum of 900°. Find its number of sides, then calculate each interior angle.
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