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Measuring Angles

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Measuring Angles

Ari is helping position lights around a small outdoor stage. Use angle facts and the diagrams to check each setup. Show calculations where you can. Angles are in degrees (°).

Read and classify angles

Classify angles using these terms: acute (less than 90°), right (90°), obtuse (between 90° and 180°), straight (180°), reflex (between 180° and 360°).

1.The stage plan labels five beam turns: 38°, 90°, 124°, 180° and 225°. Match each measurement to its angle classification.

38°
90°
124°
180°
225°

Right
Reflex
Straight
Acute
Obtuse

2.A spotlight sweeps through 87°. Which statement describes this angle?

Acute, because it is less than 90°
Right, because it is close to 90°
Obtuse, because it is more than 90°
Straight, because it is nearly half a turn

3.A technician estimates a beam turn as 179°. Is it acute, right, obtuse, straight or reflex? Explain why an estimate close to 180° is not automatically a straight angle.

Measure and calculate

Use the diagrams and angle relationships to solve the stage-plan checks.

4.The two rays in the angle diagram form an angle. Estimate its size, then write the protractor steps you would use to measure it accurately.

5.Two adjacent beams lie on a straight line. One angle is 68°. Find the other angle, x, and state the angle fact used.

6.At a rotating light mount, three angles around the centre are 95°, 142° and y°. Calculate y.

7.A stage fitting has two intersecting straight bars. One of the angles is 73°. Find the size of the vertically opposite angle and the size of either adjacent angle.

8.The light rig needs a 35° turn from its current direction. Describe how to use a protractor to mark this turn accurately, including how you avoid reading the wrong scale.

9.A full turn is 360°. A moving light has already turned 248°. How many more degrees must it turn to complete one full rotation? Classify the remaining angle.

10.Ari measures an angle as 91° with a protractor. Her teammate says it must be a right angle because it is nearly 90°. Is the teammate correct? Give a precise reason.

TrueFalse

11.A lighting designer must make a beam point in exactly the opposite direction from its starting position. What angle should the beam turn through? Explain how you know.