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Angles and Polygons Assessment

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Angles and Polygons Assessment

Show your working for calculation questions. Include degree symbols in angle answers.

Triangle angle clues

Mei is checking angle designs for a bookshop sign. Use the triangle angle sum of 180° to solve each clue.

1.A triangular sign has angles of 65° and 47°. What is its third angle?

2.A triangular shelf bracket has one angle of 60°. The other two angles are equal. Find all three angles.

3.Explain how drawing a straight line through a triangle’s three angles can help show that their total is 180°.

Polygon patterns

Freya is making a tiled display. A polygon’s interior angle sum can be found by splitting it into triangles.

4.Complete the pattern: triangle, quadrilateral, pentagon, hexagon. Write the interior angle sum for each shape.

5.A regular octagon has 8 equal sides and 8 equal interior angles. Find its interior angle sum, then calculate the size of each interior angle.

6.A five-sided display tile has interior angles 108°, 115°, 95°, 130° and x°. Find x°. (A pentagon’s interior angles total 540°.)

7.Choose the rule that gives the interior angle sum of an n-sided polygon.

(n − 2) × 180°
n × 180°
(n + 2) × 180°

8.A polygon has an interior angle sum of 900°. How many sides does it have? Show how the rule helps you decide.

Exterior angles: the turning rule

Ari walks around the outside edge of a polygon display, turning at each corner until facing the original direction again.

9.What is the sum of one exterior angle at each vertex of any polygon, when measured in the same direction?

180°
360°
It depends on the number of sides

10.An exterior angle and its adjacent interior angle lie on a straight line. If the interior angle is 128°, find the exterior angle and explain the calculation.

11.A regular hexagon has six equal exterior angles. Find the size of each exterior angle, then find each interior angle.

12.A shop display has four interior angles: 85°, 110°, 95° and a°. Find a, then find the exterior angle beside a.