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Angles and Art Measurement

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Angles and Art Measurement

Aotearoa’s community art trail needs a geometric mural. Help the design team check angles, calculate missing turns and plan a measured design. Use degrees (°). You may use a protractor and ruler for the drawing task.

Read the design plan

The mural team’s first panel has three measured angles. Use the angle guide below as a reminder: acute is less than 90°, right is 90°, obtuse is between 90° and 180°, straight is 180°, and reflex is between 180° and 360°.

1.The three marked angles in the panel are 38°, 90° and 224°. Classify each as acute, right, obtuse, straight or reflex.

2.The mural uses benchmark turns of 45°, 90°, 180° and 360°. Which one is a straight angle, and which one is a complete turn?

Calculate the joins

At a point, angles around the point add to 360°. Angles on a straight line add to 180°. A right angle is 90°.

3.Two mural strips meet on a straight line. One angle is 67°. Find the other angle and show the subtraction you used.

4.Three rays meet at a point, making angles of 128°, 96° and x°. Find x.

5.A right-angle corner in the design is divided into two angles. One is 34°. What is the other angle?

6.A stencil angle is three times 42°. Calculate its size and classify it.

Draw and design

Use the drawing space to plan a small geometric motif. Add a clear vertex and rays, then label the requested angle sizes. Your measurements should be possible to construct with a protractor.

7.Draw and label a 55° angle and a 125° angle. Name each angle type beside it.

8.Invent a simple motif using at least three angles, including one acute, one obtuse and one reflex angle. Label each with a possible measurement, then explain how your chosen measurements fit the angle types.

9.The mural designer estimates an angle at about 90°, then measures it as 87°. Is the estimate reasonable? Explain using the angle type.

10.The outside turn around a full mural panel is 360°. The design already uses turns of 72°, 108° and 95°. What turn remains?