Measurement

Angle Properties

1

Sort the Angles

Sort each angle into the correct type.

45°
90°
120°
30°
150°
75°
Acute (< 90°)
Right (= 90°)
Obtuse (> 90°)
2

Sort More Angles

Sort each angle into the correct type.

15°
90°
135°
180°
60°
110°
89°
91°
Acute
Right
Obtuse
Straight
3

Match Angle Types

Draw a line to match each angle to its type.

35°
90°
135°
180°
Straight angle
Obtuse angle
Right angle
Acute angle
4

Name the Angle Type

Circle the type for each angle.

72° is:

Acute
Right
Obtuse

145° is:

Acute
Right
Obtuse

90° is:

Acute
Right
Obtuse

88° is:

Acute
Right
Obtuse

180° is:

Obtuse
Straight
Reflex
5

Quick Angle Classification

Circle the correct classification.

An angle of 200° is:

Obtuse
Straight
Reflex

An angle of 0° is:

Zero angle
Acute
Right

An angle of 360° is:

Full turn
Straight
Reflex

An angle between 180° and 360° is:

Obtuse
Reflex
Straight
6

Estimate the Angle

Estimate the size of each angle described.

A quarter turn = ___°

A half turn = ___°

A full turn = ___°

A three-quarter turn = ___°

7

Angles on a Straight Line

Angles on a straight line add up to 180°. Find the missing angle.

One angle is 110°. The other angle = ___°

One angle is 45°. The other angle = ___°

One angle is 90°. The other angle = ___°

One angle is 63°. The other angle = ___°

8

More Angles on a Line

Find the missing angle on each straight line.

Angles are 35° and 85° and ___°. They add to 180°.

Angles are 70° and ___°. They add to 180°.

Angles are 42° and 58° and ___°. They add to 180°.

Angles are 125° and ___°. They add to 180°.

9

Angles at a Point

Angles around a point add up to 360°. Find the missing angle.

Three angles: 90°, 120°, 80°. Missing angle = ___°

Two angles: 150° and 150°. Missing angle = ___°

Four angles: 90°, 90°, 90° and ___°

10

Find the Missing Angle

Circle the correct missing angle.

Triangle: 60°, 80°, ?° (angles sum to 180°)

30°
40°
50°

Triangle: 90°, 35°, ?°

45°
55°
65°

Straight line: 125° and ?°

45°
55°
65°

Triangle: 70°, 70°, ?°

30°
40°
50°
11

More Missing Angles

Circle the correct missing angle.

Triangle: 45°, 45°, ?°

80°
90°
100°

Triangle: 30°, 60°, ?°

80°
90°
100°

Straight line: 72° and ?°

98°
108°
118°

Triangle: 55°, 65°, ?°

50°
60°
70°
12

Angles in Triangles

Find the missing angle in each triangle.

Angles: 50° and 65°. Third angle = ___°

Angles: 30° and 120°. Third angle = ___°

Angles: 72° and 72°. Third angle = ___°

An equilateral triangle has all angles equal. Each angle = ___°

13

Match Triangle Type to Angles

Draw a line to match each triangle type to its angle properties.

Equilateral
Right-angled
Isosceles
Scalene
Two equal angles
All different angles
All 60°
One 90° angle
14

Angle Problem Solving

Use angle properties to solve these problems. Show your working.

A triangle has angles of 50° and 65°. What is the third angle?

Two angles on a straight line are equal. What is each angle?

A right angle is split into two angles. One is 38°. What is the other?

The angles of a triangle are in the pattern: x, 2x, 3x. Find each angle.

15

More Angle Problem Solving

Solve each angle problem.

Two angles on a straight line are in the ratio 1:3. Find both angles.

A quadrilateral has angles of 80°, 100° and 95°. What is the fourth angle? (Angles in a quadrilateral = 360°)

An isosceles triangle has a base angle of 55°. What are the other two angles?

16

True or False: Angle Facts

Circle TRUE or FALSE.

A triangle can have two right angles

TRUE
FALSE

An obtuse triangle has one angle greater than 90°

TRUE
FALSE

The sum of angles in a quadrilateral is 360°

TRUE
FALSE

A right angle is exactly 90°

TRUE
FALSE
17

Home Activity: Angle Hunter

Find and measure angles at home!

  • 1Find 5 angles around your home. Classify each as acute, right, or obtuse.
  • 2Open a book to different widths. Estimate the angle, then check with a protractor.
  • 3Look at clock hands at different times. What angle do they make at 3:00? At 10:00?
  • 4Draw a triangle, measure all three angles with a protractor, and check they add up to 180°.
  • 5Find all the right angles in your kitchen.
18

Angles in Quadrilaterals

The sum of angles in a quadrilateral is 360°. Find the missing angle.

Angles: 90°, 90°, 110°, ?° = ___

Angles: 75°, 105°, 85°, ?° = ___

Rectangle: 3 angles are 90°. Fourth angle = ___

Parallelogram: two angles are 65°. Find the other two: ___

19

Vertically Opposite Angles

Vertically opposite angles are equal. Find the missing angles.

Two lines cross. One angle is 40°. The vertically opposite angle = ___. The adjacent angle = ___

Two lines cross. One angle is 115°. Find all 4 angles: ___

Vertically opposite angles: if 3x + 10 = 2x + 40, find x and each angle: ___

20

Co-Interior and Alternate Angles

Circle the correct relationship.

Alternate angles (Z-angles) with parallel lines are:

Equal
Supplementary
Complementary

Co-interior angles (C-angles) with parallel lines:

Add to 90°
Add to 180°
Add to 360°

Corresponding angles (F-angles) with parallel lines:

Equal
Supplementary
Add to 360°

If alternate angles = 72°, the co-interior angle =

72°
108°
118°
21

Angles in Regular Polygons

Interior angle of regular polygon = (n−2)×180° ÷ n. Calculate each.

Regular hexagon (n=6). Interior angle = ___

Regular octagon (n=8). Interior angle = ___

Regular pentagon (n=5). Interior angle = ___

Equilateral triangle (n=3). Interior angle = ___. Check with formula: ___

22

Sort by Angle Sum

Sort each polygon by the sum of its interior angles.

Triangle
Quadrilateral
Pentagon
Hexagon
180°
360°
540°
720°
23

Match Polygon to Interior Angle Sum

Draw a line to match each polygon to its interior angle sum.

Triangle
Quadrilateral
Pentagon
Hexagon
Octagon
1,080°
180°
720°
360°
540°
24

Compass Bearings and Angles

Compass bearings are measured clockwise from North.

What angle is East from North? ___. South from North? ___. West? ___

A bearing of 045° is the same as which direction? ___

You face North and turn 210° clockwise. Which direction now? ___

25

Measuring Angles with a Protractor

Estimate each angle, then describe how you'd verify with a protractor.

Estimate: A slice of pizza from a circular pie (6 slices): about ___°. Exact: ___°

Clock hands at 3:00: ___°. At 2:00: ___°. At 5:00: ___°

Clock hands at 1:30. Exact angle: ___°

26

Angle Problems with Algebra

Solve these angle problems using algebra.

Angles on a line: 2x + 30 and 3x. Find x and each angle: ___

Triangle angles: 2x, 3x, 4x. Find x and each angle: ___

Quadrilateral angles: x, x+30, 2x, 90. Find x: ___

27

Angle Facts Quiz

Circle TRUE or FALSE.

Complementary angles add to 90°

TRUE
FALSE

Supplementary angles add to 180°

TRUE
FALSE

An isosceles triangle has all angles equal

TRUE
FALSE

A regular hexagon's interior angles are each 120°

TRUE
FALSE

Angles in a pentagon add to 540°

TRUE
FALSE
28

Angle Frequency in Shapes

Count angles in these shapes. Each icon = one angle.

Triangles (3 each)
Quadrilaterals (4 each)
Pentagons (5 each)
Hexagons (6 each)
1

Which shape has the most angles?

2

For a shape with n sides, how many angles does it have?

3

If you have 2 triangles and 3 quadrilaterals, total angles = ?

29

Angle Types in a Diagram

Count and tally each type of angle in a diagram.

ItemTallyTotal
Acute (< 90°)
Right (= 90°)
Obtuse (> 90°)
Straight (= 180°)
Reflex (> 180°)
30

Angles and Parallel Lines

Two parallel lines are cut by a transversal. One angle is 65°.

Find the alternate angle: ___

Find the corresponding angle: ___

Find the co-interior angle: ___

Find the supplementary angle on the same line: ___

31

Constructing Angles

Describe how you would construct each angle accurately.

How to construct a 90° angle without a protractor: ___

How to bisect (halve) an angle: ___

32

Angles in Architecture

Answer these angle questions about buildings and design.

A roof makes a 30° angle with the ceiling. What angle does it make with the vertical wall? ___

A staircase makes a 45° angle with the floor. Each step has a tread and riser. What angle does the riser make with the horizontal? ___

33

Exterior Angles of Polygons

The sum of exterior angles of any polygon = 360°.

Each exterior angle of a regular hexagon = ___°

Each exterior angle of a regular octagon = ___°

A regular polygon has exterior angles of 40°. How many sides? ___

Interior angle + Exterior angle = ___°. Explain why: ___