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Angle Explorations Worksheet

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Angle Explorations Worksheet

Explore angles as Charlotte, Nathan and Rawiri help plan a new set of signs and paths on a dairy farm. Use angle facts, show your working, and include the degree symbol (°) in your answers.

Angle facts

Remember: angles on a straight line add to 180°. Angles around a point add to 360°. Vertically opposite angles are equal.

1.Charlotte is checking the angle where two straight farm tracks cross. One angle is 68°. What is the angle directly opposite it?

2.Nathan measures two neighbouring angles on a straight fence rail. One angle is 124°. Calculate the other angle. Show the number sentence you used.

3.At a farm gate, three angles meet at one point. They measure 95°, 130° and x°. Find x. Write the angle fact that helps you.

4.Rawiri says, “If two angles on a straight line are equal, each must be 90°.” Is Rawiri correct? Choose an answer and explain using an angle fact.

Yes. Two equal angles on a straight line are 90° each.
No. Two equal angles on a straight line are 45° each.
No. Two equal angles on a straight line are 180° each.

5.Two straight fence rails cross. One angle is 72°. Find the other three angles. Explain why two of your answers match.

6.A turn at a path junction is 90°. Is this an acute, right, obtuse or straight angle?

Acute angle
Right angle
Obtuse angle
Straight angle

7.A full turn is split into four angles: 80°, 100°, 90° and x°. Find x and check that your four angles make a full turn.

8.Draw two straight lines crossing, then label the four angles A, B, C and D. Mark one pair of vertically opposite angles with the same colour. What can you say about their sizes?

9.Nathan says an angle of 135° is acute. Is he right? Name the angle type and explain how you know.

10.Challenge: At a point on a farm sign, three angles are 2x°, 3x° and 150°. Find x, then calculate the two angles written using x.