4th Grade Measuring and Drawing Angles Worksheet Answer Key (PDF)

Q: Why is the answer to problem 18 more than 90 degrees?

A quarter turn is 90^{\circ}, and the robot then turns another 45^{\circ}. The total is 135^{\circ}, which is obtuse. To reach a half turn of 180^{\circ}, it needs 45^{\circ} more, which is the second part of the answer. A quick check like this takes only a few seconds and prevents most errors.

4th grade measuring angles worksheet answers – Maths PDF

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This 4th grade measuring angles worksheet answers covers measuring and drawing angles (Common Core 4.MD.C.5, 4.MD.C.6, 4.MD.C.7), with a free PDF to print.

Key takeaway: This answer key helps fourth grade students and parents check angle measurement and angle addition work.

Topic: Measuring and Drawing Angles (4th grade)
Content: Step-by-step answers to 20 worksheet problems
Standards: 4.MD.C.5, 4.MD.C.6, 4.MD.C.7
Answers: Every step shown, with the method to review
Format: Free printable PDF, US Letter, black and white

This answer key helps fourth grade students and parents check angle measurement and angle addition work. Also, each solution names the benchmark used, such as 90 degrees for a right angle or 180 degrees for a straight line.

The key covers all 20 problems, from the degrees in a quarter turn to the sprinkler problem about a full circle. Then, protractor answers explain which scale to read, sketches describe what a correct angle should look like, and multi step problems show each subtraction on its own line. Also, spend about 15 minutes comparing, and redo the problems where your answer differs.

Each answer shows the reasoning, the calculation, and the final angle in bold. For protractor questions, the answer says which scale to read. For sketching problems, the answer shows the finished angle so you can compare it with your own drawing.

Grade 4 · Common Core State Standards: 4.MD.C.5, 4.MD.C.6, 4.MD.C.7

4th grade measuring angles worksheet answers: worksheet problems 1 to 10

1 – Full turn

A full circle is split into 360 one-degree slices.

360°

2 – Half turn

Also, a half turn is half of a full turn: \(360 \div 2 = 180\).

180°

3 – Quarter turn

\(360 \div 4 = 90\). A quarter turn makes a right angle.

90°

4 – Three-quarter turn

One quarter is 90°, so three quarters is \(3 \times 90 = 270\).

270°

5 – Read the protractor

One ray is on 0. The other ray crosses the scale at 50. It is less than 90, so it is acute.

50°

6 – A wider angle

The second ray crosses the scale at 130. It is greater than 90, so it is obtuse.

130°

7 – Classify angles

\(35^{\circ}\) is less than 90: acute.
\(90^{\circ}\) is exactly 90: right.
\(120^{\circ}\) is more than 90: obtuse.
\(72^{\circ}\) is less than 90: acute.

acute, right, obtuse, acute

8 – Angle between two rays

Subtract the two readings: \(80 – 30 = 50\).

50°

9 – Sketch a 45° angle

Draw a ray. Put the protractor center on its endpoint and mark 45 on the scale. Draw a second ray through the mark.

A 45° angle.

A 45° angle (acute)

10 – Sketch a 120° angle

Draw a ray, line up the protractor, and mark 120 on the scale. Join the mark to the vertex.

A 120° angle.

A 120° angle (obtuse)

Worksheet problems 11 and up

11 – Add two angles

\(40 + 25 = 65\).

65°

12 – Unknown angle in a right angle

\(90 – 38 = 52\). Check: \(38 + 52 = 90\).

Also, check: 38 + 52 = 90.

52°

13 – Unknown angle on a line

\(180 – 115 = 65\). Check: \(115 + 65 = 180\).

65°

14 – Three parts

\(30 + 45 = 75\), then \(75 + 25 = 100\).

100° (obtuse)

15 – Clock hands

From 12 to 4 is 4 numbers: \(4 \times 30 = 120\).

120°

16 – Pizza slices

\(3 \times 45 = 135\).

A pizza with 8 equal slices.

135°

17 – Opening a door

\(70 + 35 = 105\). Since 105 is greater than 90, the angle is obtuse.

105°, obtuse

18 – Turning a robot

A quarter turn is 90°. Then \(90 + 45 = 135\).

A half turn is 180°: \(180 – 135 = 45\).

135°; 45° more

19 – Picture frame brace

First unknown: \(90 – 37 = 53\).

Second unknown: \(53 – 20 = 33\).

37 + 20 + 33 = 90.

53° and 33°

20 – Sprinklers

Full circle: 360°. B must sweep \(360 – 210 = 150\).

If B sweeps 90°, the dry part is \(150 – 90 = 60\).

150°; 60° dry

Key facts behind this 4th grade measuring angles worksheet answers

Key facts

An angle has two rays and one shared endpoint called the vertex.
Next, a full circle is 360 degrees, a half turn is 180 degrees, and a quarter turn is 90 degrees.
A one-degree angle turns through 1/360 of a circle.
Acute angles are less than 90 degrees, right angles are exactly 90 degrees, and obtuse angles are greater than 90 degrees.
If an angle is split into parts, the whole angle is the sum of the parts.

Common mistakes with this 4th grade measuring angles worksheet answers

Students see a protractor answer that is \(180\) minus their reading and assume the key is wrong. Check whether you read the outer scale instead of the inner scale.
Students check only sketches by eye. Also, remeasure your drawn angle for problems 9 and 10 and accept a difference of about two degrees.
Students skip the classification part in problem 17. Instead, the key asks whether \(105^{\circ}\) is acute or obtuse, and that label is part of the answer.
Students copy the answer to problem 20 without checking it. The two sprinklers must add to \(360^{\circ}\), so add your answer to \(210^{\circ}\) to confirm.

How to use these solutions

Check each answer by adding the parts. Finally, if a right angle is split into two parts, they should total 90, and a straight line should total 180.
For protractor problems, say which scale you used. Also, this helps you spot the common mistake of reading from the wrong zero.
Parents can ask the child to explain why a half turn is \(180^{\circ}\), using a spinning chair or a door swing as an example.

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4th grade measuring angles worksheet answers: frequently asked questions

What if my protractor reading is a degree or two off?

Small differences are normal because pencil lines have thickness and protractors are hard to line up exactly. So, most teachers accept a reading within two degrees. Also, if your answer is off by more, recheck that the center is on the vertex and zero is on a ray.

Why is the answer to problem 18 more than 90 degrees?

A quarter turn is \(90^{\circ}\), and the robot then turns another \(45^{\circ}\). The total is \(135^{\circ}\), which is obtuse. To reach a half turn of \(180^{\circ}\), it needs \(45^{\circ}\) more, which is the second part of the answer. A quick check like this takes only a few seconds and prevents most errors.

How can I check an unknown angle answer quickly?

Add the unknown angle to the known angle or angles and compare with the total. For problem 13, \(65 + 115 = 180\), so the answer fits a straight line. This one step catches most arithmetic slips. A quick check like this takes only a few seconds and prevents most errors.

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