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Angles and Measurement Exploration

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Angles and Measurement Exploration

At a marae visit, Losa, Talia and Ari are helping plan a safe route through a welcome display. Use angle facts and careful calculations to solve each task. A full turn is 360°, a straight line is 180°, and a right angle is 90°. Show working for calculations.

1 | Angle clues

Start with the angle rules, then use them to read the plans.

1.At the entrance, four sign panels meet at one point. Three angles are 78°, 96° and 104°. Calculate the fourth angle, then classify it as acute, right, obtuse or straight.

2.A straight decorative beam is divided by a support. One angle is 127°. What is the angle on the other side of the support?

3.Two paths cross on the welcome map. The top angle is 68°. What is the vertically opposite angle? Explain the rule you used.

4.Which statement is correct about angles around a point?

They add to 90°
They add to 180°
They add to 360°
They are always equal

2 | Measure and design

Use the diagrams and measurements to plan the display.

5.The pointer on a layout drawing turns from north to east. What angle has it turned through?

6.Talia is drawing a 135° corner for a floor pattern. In the drawing box, sketch an angle of about 135° and label it. Then state whether it is acute, right or obtuse.

7.A circular pattern is split into 8 equal sections. Calculate the angle at the centre of each section.

8.A carved border is 2.4 m long. Talia has placed 165 cm of trim. How many centimetres of trim are still needed?

9.A route sign points along a straight path. Its arrow turns 38° from the path in one direction. What is the angle between the arrow and the path in the opposite direction?

3 | Explain your thinking

Use precise angle language in your answers.

10.Ari says, “If one angle where two straight lines cross is 112°, the angle beside it is also 112°.” Is Ari correct? Find the adjacent angle and explain.

11.Complete the rule: When two straight lines intersect, vertically opposite angles are , and adjacent angles on a straight line add to .

12.Create one angle puzzle for another visitor using a straight line or a full turn. Include enough information to calculate a missing angle, and write its solution.