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Angles and Measurement Exploration

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Angles and Measurement Exploration

A community festival is being set up in Aotearoa New Zealand. Use angle facts to check the layout, solve the clues and design one feature. Show working where you can. You will need a protractor for the drawing task.

Angle toolkit

Use precise angle vocabulary to help the festival crew communicate.

1.Match each angle term to its meaning: acute; right; obtuse; straight. Meanings: A. exactly 90°; B. greater than 90° and less than 180°; C. less than 90°; D. exactly 180°.

Acute
Right
Obtuse
Straight

D. Exactly 180°
B. Greater than 90° and less than 180°
C. Less than 90°
A. Exactly 90°

2.A path junction has an angle of 128°. Which description fits it best?

Acute
Right
Obtuse
Straight

3.At a crossing of two straight paths, one angle is 73°. Find the vertically opposite angle and the angle next to it on the straight line. Explain which angle facts you used.

Solve the site-plan clues

Use the angle relationships in each setup. Angles around a point total 360°.

4.Two straight paths cross. One angle is 64°. What is the size of the adjacent angle on the straight line?

5.Four angles meet at the centre of a circular stage. Three measure 82°, 95° and 104°. Find the fourth angle.

6.A signpost makes an angle of 38° with a straight pavement edge. The other angle on that straight line is x°. Write an equation and solve for x.

7.Three paths meet at a point. Their three angles are in the ratio 1:2:3. Find each angle. Remember that a full turn is 360°.

Measure and design

Accurate measurement helps make a safe, easy-to-follow festival layout.

8.The entrance gate is designed to open to 60°. Use a protractor to draw an angle of exactly 60°. Label the vertex and both arms.

9.The two arms of a decorative banner meet at the shown angle. Estimate its size, then measure it with a protractor. Record both answers and find how many degrees your estimate differs from the measurement.

10.A volunteer says, “The four angles around the middle of a round table add to 180°.” Is this correct? Explain the correct total and why.

11.Create a small plan for a festival feature made from two straight paths crossing. Draw the crossing, label one angle 70°, and mark the other three angles with their correct sizes. Name one angle relationship that helped you.