Angles Worksheets

An angle is the amount of turn between two lines that meet at a point, and it is measured in degrees. The three PDFs on this page ask children to sort angles as acute, right, obtuse or straight, and every sheet has an answer key. They follow standard 4.G.A.1 of the Common Core standards for grade 4 geometry, and the notes below explain the types, how to compare an angle with a right angle, and how to measure with a protractor.

Quick answer: An angle is the amount of turn between two lines that meet at a point. An acute angle is less than 90°, a right angle is exactly 90°, an obtuse angle is more than 90° and less than 180°, and a straight angle is 180°. This page has 3 free printable angles worksheets with answer keys. Updated October 2026.

Compare with a right angle

A right angle is a square corner, like the corner of a sheet of paper. Use it to compare: an acute angle is smaller (sharper), an obtuse angle is bigger (more open) and a straight angle is a straight line. Children can hold the corner of a card against each angle on the worksheet to check.

Angles worksheets: what is in the set

There are 3 angles worksheets on this page, and every one has an answer key except for any cut-out games. Each set has 12 to sort, and the first set also includes straight ones.

Angles: parts, units and types

An angle is made of two arms that meet at a vertex. The size of an angle is the amount that one arm turns to reach the other, and it is measured in degrees, with 360 degrees in a full turn. Wikipedia’s article on angles gives the history of the degree. This table shows the types of angle that children meet, with the size, a way to remember it and an example:

The worksheets on this page use the first four types: acute, right, obtuse and straight. Reflex and full turns appear in grade 5 and 6.

Acute obtuse right angles worksheet: sorting by size

The acute obtuse right angles worksheet asks children to compare each angle with a right angle. A right angle is the corner of a sheet of paper, and it is exactly 90°. An angle that fits inside the corner is acute, and an angle that is wider than the corner is obtuse. This table shows twelve angles that are like those on the first sheet, with the comparison and the type:

The angles 89° and 91° are very close to 90°, and children cannot tell them from a right angle by eye, so a right-angle tester or a protractor is needed for angles like these.

Types of angles worksheet: angles in everyday life

A types of angles worksheet is easier when children can link each type to something they know. A corner of a book is a right angle, the tip of a slice of pizza is acute, a laptop that is open wide is obtuse, and the edge of a ruler is straight. The clock is the best everyday example, because the angle between the hands is a multiple of 30° at every hour. This table shows the angle at each o’clock time:

At 3:00 and 9:00 the hands make a right angle. At 6:00 they make a straight line. At 12:00 the hands lie on top of each other, so there is no angle between them. The telling time worksheets page uses the same clock faces.

Classifying angles: using the right angle as a benchmark

When classifying angles, the best tool is a right-angle tester: fold a sheet of paper twice to make a square corner. To use it, place the corner on the vertex, and line up one edge with one arm of the angle. If the other arm is inside the corner, the angle is acute. If it is on the edge, the angle is a right angle. If it is outside, the angle is obtuse. Children can also use the fractions of a turn, which this table shows:

Each of these is a fraction of 360°, so classifying angles is also a use of fractions. The identifying fractions page has the same fractions on shapes, and the fractions worksheets cover the arithmetic.

Angles grade 4: the standards

For angles grade 4, there are four standards, two in geometry and two in measurement. The first, 4.G.A.1, is about drawing and identifying angles, and it is the one that the worksheets on this page practice. The next three are about measuring. This table lists them, and the Common Core standards for grade 4 measurement and data list the rest of the measurement standards:

The additive idea in 4.MD.C.7 is used to find a missing angle. The three corners of a triangle always add up to 180°, and the table below shows six triangles with their types:

Drawing an angle with a set square

Standard 4.MD.C.6 also asks children to draw an angle of a given size, and a set square is a quick way to do it. A set square is a plastic triangle with fixed corners. The two common kinds have the corners 45°, 45° and 90°, and 30°, 60° and 90°. Every corner of both is a size that can be traced. By putting two corners next to each other, or by taking one from another, children can make more sizes. This table shows what can be made from the four sizes 30°, 45°, 60° and 90°:

The sums give the obtuse sizes, such as 105° and 135°, and the differences give the small sizes, such as 15°. A child who has a set square and a pencil can draw all of these without a protractor, and can check a protractor reading against them.

Measuring angles with a protractor: step by step

A protractor is a half circle with a scale of 0° to 180°, and most have two scales, one that starts at 0 on the right and one that starts at 0 on the left. Children follow these steps:

1. Put the center hole of the protractor on the vertex of the angle.
2. Line up the base line of the protractor with one arm of the angle, so that the arm points to 0.
3. Find the scale that starts at 0 on that arm.
4. Follow the other arm to the scale, and read the number.
5. Check with the type: an acute angle must be less than 90°, and an obtuse angle must be more than 90°.

The last step stops the most common error, which is reading the wrong scale. If the angle is 50°, the other scale reads 130°, and a child who checks that the angle is acute knows that 130° cannot be right. This table shows six angles, with the right reading and the wrong one:

Common mistakes with angles

The most common mistake is to think that longer arms make a bigger angle. This table shows five mistakes, what went wrong and the fix:

Angles word problems

Angles appear in pizza, clocks, doors and triangles. Ask children to draw each angle, to compare it with a right angle, and to name the type:

Games and activities for angle measure

Children learn angle measure best when they play with it. These games use things that are found at home or in a classroom:

• Right-angle hunt: find right angles in the room with a paper tester, and write down where they are
• Human arms: two children are the arms, and a third child says whether the angle is acute, right or obtuse
• Clock angles: set a clock to a time, and ask what type of angle the hands make
• Angle bingo: a bingo card with angle types, and calling cards with drawings
• Straw hinge: make an angle with two straws and a pin, and open it to match a type
• Angle sort: sort a pack of angle cards into acute, right and obtuse

Extra support and extra challenge with angle measure

For children who need more support: make a right-angle tester from a folded sheet of paper, and use it on every angle. Do the first set only, and sort the angles into two groups: smaller than the corner, and bigger than the corner. Add the right angle and the straight angle once the child is sure of the two groups.

For children who need more challenge: ask for the angle between the hands of a clock at 4:30, for three angles that make a straight line, and for the third angle of a triangle with angles of 35° and 80°. Measuring with a protractor, and drawing an angle of 70°, are good challenges.

How to tell that a child is ready to move on from angle measure

1. The child compares an angle with a right angle using a tester.
2. The child names acute, right, obtuse and straight angles.
3. The child links each type to the size in degrees.
4. The child measures an angle with a protractor and checks the type.

When all four are true, move on to the symmetry page, or go back to the 2D shapes page to find the angles in shapes.

A 20-minute lesson on angle measure

A short lesson is the best way to introduce angle measure. This 20-minute plan can be used in a classroom, at a tutoring session or at home, and it uses the worksheets at the end:

Where angle measure fits across the grades

No skill stands alone. This table shows what children learn before and after angle measure, with the standard that goes with each step:

This page is the last in the geometry sequence for grade 4. The whole sequence is on the geometry worksheets page.

Helping at home with angle measure

Parents do not need to be experts to help with angle measure. These suggestions work well, and each takes only a few minutes:

• Look for right angles at home: books, doors, windows, tables.
• Open a laptop to different angles and name each.
• Use a clock: “what type of angle do the hands make at 4:00?”
• Make a right-angle tester together from a sheet of paper.
• Praise “I checked with the corner”.

How to check progress in angle measure

A teacher or parent can check progress with the answer key and a few questions. This table shows three common situations, what they mean and what to do next:

A five-day plan for angle measure

Most children need about a week of short sessions for angle measure. This plan follows the order of the worksheets on this page:

When the plan is complete, the child is ready for the grade 4 measurement standards. The whole sequence is on the geometry worksheets page.

Angles worksheet: classify these angles

Here is a short angles worksheet with the answers shown, which also works as an angle classification worksheet or an angle identification worksheet. Cover the second column and name each type of angle, then check:

This page is also searched as angle worksheets, worksheets on angles, measure of angles worksheet, measuring angles sheet, names of angles worksheet, classification of angles worksheet, kinds of angles worksheet, measure angles worksheet and triangle angles worksheet. All are the free PDFs above. For triangle angles, remember that the three angles add up to 180°. An angles activity sheet can be a hunt around the room for right angles in doors, books and windows.