Angle Properties
Sort the Angles
Sort each angle into the correct type.
Sort More Angles
Sort each angle into the correct type.
Match Angle Types
Draw a line to match each angle to its type.
Name the Angle Type
Circle the type for each angle.
72° is:
145° is:
90° is:
88° is:
180° is:
Quick Angle Classification
Circle the correct classification.
An angle of 200° is:
An angle of 0° is:
An angle of 360° is:
An angle between 180° and 360° is:
Estimate the Angle
Estimate the size of each angle described.
A quarter turn = ___°
A half turn = ___°
A full turn = ___°
A three-quarter turn = ___°
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 = ___°
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°.
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 ___°
Find the Missing Angle
Circle the correct missing angle.
Triangle: 60°, 80°, ?° (angles sum to 180°)
Triangle: 90°, 35°, ?°
Straight line: 125° and ?°
Triangle: 70°, 70°, ?°
More Missing Angles
Circle the correct missing angle.
Triangle: 45°, 45°, ?°
Triangle: 30°, 60°, ?°
Straight line: 72° and ?°
Triangle: 55°, 65°, ?°
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 = ___°
Match Triangle Type to Angles
Draw a line to match each triangle type to its angle properties.
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.
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?
True or False: Angle Facts
Circle TRUE or FALSE.
A triangle can have two right angles
An obtuse triangle has one angle greater than 90°
The sum of angles in a quadrilateral is 360°
A right angle is exactly 90°
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.
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: ___
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: ___
Co-Interior and Alternate Angles
Circle the correct relationship.
Alternate angles (Z-angles) with parallel lines are:
Co-interior angles (C-angles) with parallel lines:
Corresponding angles (F-angles) with parallel lines:
If alternate angles = 72°, the co-interior angle =
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: ___
Sort by Angle Sum
Sort each polygon by the sum of its interior angles.
Match Polygon to Interior Angle Sum
Draw a line to match each polygon to its interior angle sum.
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? ___
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: ___°
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: ___
Angle Facts Quiz
Circle TRUE or FALSE.
Complementary angles add to 90°
Supplementary angles add to 180°
An isosceles triangle has all angles equal
A regular hexagon's interior angles are each 120°
Angles in a pentagon add to 540°
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) |
Which shape has the most angles?
For a shape with n sides, how many angles does it have?
If you have 2 triangles and 3 quadrilaterals, total angles = ?
Angle Types in a Diagram
Count and tally each type of angle in a diagram.
| Item | Tally | Total |
|---|---|---|
Acute (< 90°) | ||
Right (= 90°) | ||
Obtuse (> 90°) | ||
Straight (= 180°) | ||
Reflex (> 180°) |
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: ___
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: ___
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? ___
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: ___