Angles in Degrees
Sort the Angles (A)
Sort each angle into the correct type.
Sort the Angles (B)
Sort each angle.
Match Angles to Descriptions
Draw a line from each angle type.
Identify the Angle Type (A)
Circle the angle type.
35° is a...
90° is a...
145° is a...
180° is a...
Identify the Angle Type (B)
Circle the angle type.
89° is...
91° is...
1° is...
179° is...
Angle Sequence
Fill in the missing angles counting by 45°.
Angle Bonds to 90°
Two angles make a right angle. Find the missing angle.
Angle Bonds to 180°
Two angles make a straight line. Find the missing angle.
Name That Angle
Write whether each angle is acute, right, obtuse, straight or reflex.
52° is ___
90° is ___
167° is ___
180° is ___
250° is ___
Estimate the Angle (A)
Circle the best estimate for each angle.
A corner of a book is...
Half a right angle is...
A straight line is...
A quarter turn is...
Estimate the Angle (B)
Circle the best estimate.
The angle between clock hands at 2 o'clock is about...
The angle of an open laptop screen is about...
A slice of pizza (1/8 of the whole) has an angle of...
The angle at the tip of an equilateral triangle is...
Calculate Missing Angles (A)
Angles on a straight line add up to 180°.
Two angles on a straight line: one is 60°. The other is ___°
Two angles on a straight line: one is 110°. The other is ___°
A right angle is divided into two parts. One is 35°. The other is ___°
Three angles on a straight line: 40°, 50° and ___°
Calculate Missing Angles (B)
Angles around a point add up to 360°.
Three angles around a point: 120°, 90° and ___°
Two angles around a point: 200° and ___°
Four angles around a point: 80°, 100°, 70° and ___°
Match Angles to Turns
Draw a line from each turn to its angle.
Angles in Shapes (A)
Use angle facts to find missing angles.
A triangle has angles of 60° and 80°. The third angle is ___° (angles in a triangle = 180°)
A triangle has angles of 45° and 45°. The third angle is ___°
A triangle has a right angle and a 35° angle. The third angle is ___°
Angles in Shapes (B)
Find the missing angles.
A rectangle has four ___° angles
A square has angles totalling ___°
An equilateral triangle has three angles of ___° each
The angles in any quadrilateral add up to ___°
Angle Facts True or False
Circle TRUE or FALSE.
Angles in a triangle always add up to 180°
A right angle is exactly 90°
Angles on a straight line add up to 180°
An equilateral triangle has three equal angles
Angle Problems (A)
Solve each problem. Show your working.
A triangle has angles of 60° and 80°. What is the third angle? What type of triangle is this?
A clock shows 3 o'clock. What angle do the hands make? What about at 6 o'clock?
Two angles in a triangle are both 45°. What is the third angle? What type of triangle is this?
Angle Problems (B)
Solve these problems.
Two straight lines cross. One angle is 70°. Find the other three angles.
A quadrilateral has angles of 80°, 110° and 95°. What is the fourth angle?
Clock Angles
Calculate the angle between clock hands.
At 1 o'clock: ___°
At 4 o'clock: ___°
At 6 o'clock: ___°
At 9 o'clock: ___°
What pattern do you notice? Each hour = ___°
Design with Angles
Use angles to answer these.
A pizza is cut into 8 equal slices. What angle is each slice?
A spinner has 5 equal sections. What angle is each section?
A pie chart shows 25% for sport. What angle does the sport section have?
Create Angle Problems
Write your own angle problems.
Write a problem about missing angles on a straight line. Then solve it.
Write a problem about angles in a triangle. Then solve it.
Angle Bonds to 360°
Angles around a point add to 360°. Find the missing angle.
Angles in Quadrilaterals
Angles in a quadrilateral add up to 360°.
A quadrilateral has angles 90°, 90°, 90° and ___°
A quadrilateral has angles 80°, 100°, 70° and ___°
A parallelogram has two angles of 60°. What are the other two angles?
Estimate Angles in Real Life
Circle the best estimate.
Angle of an open book
Angle of a ramp for a wheelchair
Angle of a roof peak
Angle you turn when making a U-turn
Angle Calculations (A)
Calculate each missing angle.
A right angle divided into 3 equal parts: each angle = ___°
A straight angle divided into 4 equal parts: each angle = ___°
A full turn divided into 8 equal parts: each angle = ___°
Two complementary angles: one is 25°, the other is ___°
Angle Calculations (B)
Find the missing angles.
Supplementary angles: one is 65°, the other is ___°
Vertically opposite angles: if one is 110°, the opposite angle is ___°
An isosceles triangle has a base angle of 50°. What are all three angles?
Sort Angles by Size
Sort these angles from smallest to largest.
Match Angles to Fractions of a Turn
Draw a line.
Interior Angles of Regular Shapes
Circle the interior angle.
Each angle in an equilateral triangle
Each angle in a square
Each angle in a regular hexagon
Angle Word Problems
Solve these.
Two angles on a straight line are in the ratio 1:2. What are the two angles?
A triangle has one angle of 90°. The other two are equal. What are they?
A reflex angle and its non-reflex pair add to 360°. If the reflex angle is 250°, what is the other?
Compass Directions and Angles
Compass turns are measured in degrees.
North to East is a turn of ___°
North to South is a turn of ___°
North to West (clockwise) is a turn of ___°
North to North-East is a turn of ___°
Identify the Angle Type (C)
Circle the angle type.
15° is...
90° is...
170° is...
200° is...
Identify the Angle Type (D)
Circle the angle type.
360° is a...
100° is...
270° is a...
45° is...
Name That Angle (B)
Write the angle type.
22° is ___
90° is ___
135° is ___
180° is ___
300° is ___
360° is ___
Sort the Angles (C)
Sort each angle.
Angle Bonds to 90° (B)
Find the missing angle to make a right angle.
Angle Bonds to 180° (B)
Find the missing angle to make a straight line.
Match Angles to Types (A)
Draw a line.
Estimate the Angle (C)
Circle the best estimate.
The angle of a skateboard ramp
The angle at the point of a kite
Angle between hands at 5 o'clock
The angle of a slide in a playground
Calculate Missing Angles (C)
Find the missing angle.
Three angles on a straight line: 55°, 65° and ___°
Four angles around a point: 90°, 90°, 80° and ___°
Two angles on a straight line: one is three times the other. What are they?
Angles in Shapes (C)
Find missing angles.
A triangle has angles 40° and 70°. Third angle: ___°. What type of triangle?
A quadrilateral has angles 90°, 80° and 110°. Fourth angle: ___°
A regular pentagon: sum of angles = ___°. Each angle = ___°
Angle Facts (B)
Circle TRUE or FALSE.
Vertically opposite angles are equal.
Angles in a quadrilateral add to 180°.
A reflex angle is more than 180°.
Complementary angles add to 90°.
Clock Angles (B)
Calculate the angle.
At 2 o'clock: ___°
At 5 o'clock: ___°
At 10 o'clock: ___°
At 8 o'clock: ___° (smaller angle)
Match Clock Times to Angles
Draw a line.
Angle Problems (C)
Solve.
In a right-angled triangle, one angle is 35°. What is the third angle?
The angles of a triangle are in the ratio 1:2:3. Find all three angles.
Two lines cross making an angle of 55°. Find all four angles at the intersection.
Angle Reasoning
Explain your thinking.
Why can a triangle never have two obtuse angles?
Can a triangle have two right angles? Explain.
What is the maximum number of acute angles a quadrilateral can have?
Angle Bonds to 270°
Three right angles make 270°. Find the missing angle.
Interior Angles of Polygons
Use the formula (n-2) × 180° for the sum of interior angles.
Triangle (3 sides): sum = ___°
Quadrilateral (4 sides): sum = ___°
Pentagon (5 sides): sum = ___°
Hexagon (6 sides): sum = ___°. Each angle in a regular hexagon = ___°
Angle Problems — Mental Maths
Circle the correct answer.
Two angles on a straight line: 75° and ___°
Three equal angles in a triangle: each is ___°
Angles around a point: 3 equal angles, each is ___°
A pentagon has angle sum ___°
Match Angle Types to Degree Ranges
Draw a line.
Sort Angles into Types
Sort each angle.
Angle Problems (D)
Find the missing angles.
Angles in a quadrilateral: 85°, 95°, 100° and ___°
Angles in a pentagon: 110°, 120°, 100°, 90° and ___°
A triangle has angles in ratio 1:2:3. What are the three angles?
Angles on a Grid
Use coordinate grid directions.
Moving from (0,0) directly right then directly up traces an angle of ___°
A diagonal line from (0,0) to (3,3) makes an angle of ___° with the horizontal
Two lines at 90° to each other are called ___
Angle Types in Architecture
Count angle types found in a building survey.
| Right angles | |
| Acute angles | |
| Obtuse angles | |
| Reflex angles |
What type appeared most?
Total angles counted?
What fraction are right angles?
Why are right angles so common in buildings?
Angle Estimates
Students estimated angles in a picture. Count their answers.
| Item | Tally | Total |
|---|---|---|
Acute | ||
Right | ||
Obtuse | ||
Reflex |
Angle Patterns
Find patterns in angles.
Each interior angle of a regular triangle = ___°. Each interior angle of a regular hexagon = ___°. Each interior angle of a regular 12-gon = ___°.
As the number of sides increases in a regular polygon, what happens to each interior angle? ___
Angles in Everyday Life
Estimate angles in each situation.
The angle of a typical staircase step (rise/run): about ___°
The angle of a car's windshield: about ___°
The angle you lean when cycling around a corner: about ___°
Find 2 right angles and 2 obtuse angles in your home. Describe where they are.
Angle Facts (C)
Circle TRUE or FALSE.
The sum of angles in any triangle is always 180°.
A reflex angle is between 90° and 180°.
Angles in a hexagon sum to 720°.
All right angles are equal to 90°.
Using a Protractor
Describe how to measure an angle with a protractor.
Step 1: Place the protractor's ___ point on the vertex of the angle.
Step 2: Align the ___ line with one arm of the angle.
Step 3: Read the scale where the ___ arm crosses the curved edge.
If an angle looks obtuse but you read 40°, you should read the ___ scale instead.
Angle Investigation
Investigate angle sums.
Draw any quadrilateral. Measure all four angles. Sum = ___°. Is this always 360°?
Draw any triangle. Tear off the corners. Arrange them along a straight line. What do you notice?
Match Angle to Degrees (B)
Draw a line.
Supplementary Angle Bonds
Two supplementary angles add to 180°. Find the missing angle.
Angles in Triangles (B)
Find the missing angle in each triangle.
45°, 75°, ___°
90°, 35°, ___°
120°, 30°, ___°
55°, 55°, ___°
72°, 48°, ___°
Angles in Quadrilaterals (B)
Find the missing angle in each quadrilateral (angles sum to 360°).
90°, 90°, 80°, ___°
100°, 110°, 70°, ___°
120°, 120°, 60°, ___°
95°, 85°, 105°, ___°
Sort Angles (D)
Sort each into the correct range.
Angle Types in Polygons
Circle the correct answer.
A regular hexagon has interior angles of ___°.
A regular pentagon has interior angles of ___°.
A regular octagon has interior angles of ___°.
A regular decagon (10 sides) has interior angles of ___°.
Angles and Bearings Introduction
Bearings are measured clockwise from North.
North = 000°. East = ___°. South = ___°. West = ___°.
North-East = ___°. South-East = ___°. South-West = ___°.
A ship sails on a bearing of 090°. Which direction is it going? ___
Measuring Angles Practice
Estimate the following angles.
A door opened to about 1/4 open: ___°
A door opened flat against a wall: ___°
The minute hand from 12 to 3 on a clock: ___°
An equilateral triangle corner: ___°
Angles Measured in Architecture
Students measured angles in a school building.
| 90° (right) | |
| 45° (acute) | |
| 135° (obtuse) | |
| Other |
Most common angle?
Total angles measured?
What fraction are right angles?
Why do buildings use mostly right angles?
Angle Estimation Accuracy
Students estimated an angle of 60°. Count how close they were.
| Item | Tally | Total |
|---|---|---|
Within 5° | ||
5-10° off | ||
10-20° off | ||
More than 20° off |
Angle Problems (E)
Solve these harder problems.
A clock shows 2:30. What angle do the hands make (consider the minute and hour hand positions)?
A gear rotates 40° each second. How many full rotations in one minute?
If you draw a diagonal in a square, it divides each corner angle into two equal angles. What is each small angle?
Design With Angles
Use angle knowledge to design shapes.
Design a logo using only right angles. Describe it.
Design a pattern using only 60° angles. Describe it.
Compare Angle Sizes
Which angle is larger?
75° or 60°?
135° or 150°?
90° or 89°?
Match Angle Name to Size Range
Draw a line.
Co-interior Angle Bonds
Co-interior angles (same side of a transversal) add to 180°.
Angles in Polygons (B)
Circle the correct answer.
Sum of interior angles of a triangle?
Sum of interior angles of a quadrilateral?
Each angle of a regular hexagon?
Sum of exterior angles of any convex polygon?
Sort Angles: Acute, Right, Obtuse, or Reflex?
Sort each angle measurement.
Finding Unknown Angles (C)
Find the missing angles using angle rules.
Angles on a straight line: 35° + 75° + n° = 180°. n = ___
Vertically opposite angles: if one angle is 64°, the opposite angle is ___
A triangle has angles 48° and 65°. Third angle: ___
A quadrilateral has angles 90°, 85°, and 110°. Fourth angle: ___
Angles in Navigation
Compass bearings use angles.
North is 0°, East is 90°. What is South? ___ West? ___
A ship turns from North to 135°. What direction is this (between which compass points)? ___
Turn 270° clockwise from North. Where are you now? ___
Angle Sequences
Continue each angle sequence.
Compare Angle Types
Tick which angle is larger.
75° (acute) vs 115° (obtuse)
135° (obtuse) vs 200° (reflex)
Clock Angles (B)
Calculate angles made by clock hands.
At 3:00, the angle between the hands is ___°
At 6:00, the angle between the hands is ___°
At 12:00, the angle between the hands is ___°
At 2:00, the angle between the hands is ___°
Angles Found in Nature
A student measured angles found in nature.
| Leaf veins (acute) | |
| Crystal structures (90°) | |
| Flower petal angles (72°) | |
| Branch angles (obtuse) |
Most common type of angle in nature?
Total angles measured?
Flower petals: 5 petals × 72° = total around centre?
What angle type do branch angles fall into?
Angles in Sport
Angles are important in sport.
A basketball free throw at 45° gives the best arc. What type of angle is 45°? ___
A skiing slalom course has gates. At a 30° angle the skier must turn. At 90° at the bottom. What is the turn type? ___
Describe one other sport where angles are important:
Angle Names and Properties (B)
Match each angle name to its size range.
Angles in a Triangle (B)
Find the missing angle.
Angle Types in Polygons
Circle the correct answer.
All angles in a square are...
A regular hexagon's interior angles are each...
The sum of angles in a quadrilateral is...
A regular triangle's angles are each...
Sort by Angle Size
Sort from smallest to largest angle.
Angles Around a Point
Angles around a point sum to 360°.
Three angles meet at a point: 120°, 95°, and n°. Find n: ___
Four equal angles meet at a point. Each angle: ___
Draw a diagram showing 4 angles around a point that sum to 360°:
Using a Protractor (B)
Describe how to measure angles accurately.
List the 4 steps for measuring an angle with a protractor:
A student measured 55° but the actual angle was 125°. What mistake did they make? ___
Angle Patterns (B)
Continue each angle sequence.
Angles in Architecture (B)
Architects use angles when designing buildings.
A roof makes a 35° angle with the ceiling. What is the angle on the other side (supplementary)? ___
A staircase rises at 40° to the floor. What is the angle between the staircase and the wall? ___
Why are right angles (90°) so common in buildings?
Compare Angle Measures (B)
Which angle is larger?
80° vs 100° — which is larger?
45° vs 135° — which is larger?
Angle Types in a Building
Count angle types found in a floor plan.
| Item | Tally | Total |
|---|---|---|
Right angles (90°) | ||
Acute angles (<90°) | ||
Obtuse angles (>90°) | ||
Straight lines (180°) |
Home Activity: Angle Scavenger Hunt
Find angles all around you!
- 1Find 3 right angles in your home (corners of doors, books, tiles).
- 2Open a door to different angles. Estimate the angle.
- 3Look at the hands on an analogue clock at different times. Estimate the angle.
- 4Fold a piece of paper to make angles of 45°, 90° and 180°.