4th Grade · 4.MD.C.7

Missing angles in 4th grade

Missing angles problems show an angle split into parts and ask for the size of one part. In 4th grade, your child learns that the parts of an angle add up to the whole angle. Your child uses that fact to find the missing angle with addition or subtraction, often by writing an equation.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

4.MD.C.7 Recognize angle measure as additive. When an angle is decomposed into non-overlapping parts, the angle measure of the whole is the sum of the angle measures of the parts. Solve addition and subtraction problems to find unknown angles on a diagram in real world and mathematical problems, e.g., by using an equation with a symbol for the unknown angle measure.

What it means, in plain words

An angle is the turn between two rays that share a starting point, and it is measured in degrees. When a ray splits an angle into two parts that do not overlap, the two smaller angles add up to the big one. Some worksheets call this idea additive angles: angle measures can be added and subtracted like lengths.

Adding angles answers questions such as how far a door has turned after two pushes. Finding unknown angles goes the other way. If your child knows the whole angle and one part, subtracting gives the missing part. Two numbers come up in most missing angles problems. A square corner, called a right angle, is $90^\circ$ . A straight line makes an angle of $180^\circ$ .

In 4th grade, your child writes an equation with a letter or a box for the unknown angle, such as $a + 40 = 90$ . The letter stands for the number of degrees that is missing.

Your child should be able to:

Explain that the parts of an angle add up to the whole angle
Add two angle measures to find a whole angle
Find a missing angle by subtracting from the whole angle, from $90^\circ$ or from $180^\circ$
Write an equation with a letter for the unknown angle and solve it

Example

A door opens $45^\circ$ . Then someone pushes it open another $30^\circ$ . How far has the door turned in all?

The two turns sit side by side, so the angles add.
$45 + 30 = 75$
The door has turned $75^\circ$ in all.

Example

A ray splits a straight line into two angles. One angle measures $112^\circ$ . What does the other angle, $a$ , measure?

A straight line makes an angle of $180^\circ$ , so the two parts add up to 180.
Write the equation: $112 + a = 180$ .
$a = 180 - 112 = 68$
The missing angle measures $68^\circ$ .

Where children usually get stuck

The whole angle is $130^\circ$ and one part is $50^\circ$ , and your child writes $180^\circ$ for the missing part.
The child sees two numbers and adds them without asking which one is the whole. A part has to be smaller than the whole.
What helps. Ask your child to trace the whole angle with a finger, then the known part. Then ask whether the missing piece is bigger or smaller than the whole. Smaller means subtract: $130 - 50 = 80$ .
Your child cannot start when the diagram shows two angles on a straight line, because no number is given for the whole.
The $180^\circ$ is not written anywhere. The child has to know that a straight line is a half turn.
What helps. Fold a sheet of paper in half and open it. The fold makes a straight line, a half turn of $180^\circ$ . Fold it again the other way to see two right angles, $90 + 90 = 180$ .
Your child measures each part with a protractor, adds the readings and gets a total a degree or two away from the whole angle given in the problem.
Protractor readings are close but not exact. When the diagram gives the numbers, the answer comes from adding or subtracting, not from measuring.
What helps. Ask whether the problem gives numbers. If it does, put the protractor away and write the equation first.

Try four practice questions

Real 4th grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
The angle below is split into two parts. The measure of each part and the measure of the whole angle are labeled.
Drag tiles into the blanks to build an equation that matches the diagram.
Tap or click a tile to drop it into the highlighted blank, or tap an empty blank first to choose a different one. Tap a filled blank to send its tile back.
120
70
100
-
+
20
50
=
Tap an item to place it in the next empty slot, or drag it to a specific slot. With a keyboard: select an item with Enter or Space, then select a slot to place it. Press Delete or Backspace on a slot to remove an item.
Show the answer and how to solve it
The equation $50 + 70 = 120$ matches the diagram. The two part angles ( $50°$ and $70°$ ) add up to make the whole angle ( $120°$ ).
1. 1Look at the diagram. The whole angle measures $120°$ , and it is split into two smaller parts that measure $50°$ and $70°$ .
2. 2Angle measures are additive: when an angle is split into smaller parts, the part measures add together to equal the whole.
3. 3Build the equation by placing the two part measures on the left of the equals sign with a plus tile between them, and the whole measure on the right.
Common mistake. A common mistake is dragging the minus tile instead of the plus tile, or placing the whole angle on the left of the equals sign. The two part angles combine to make the whole, so the whole comes after the equals sign and the operation between the parts is addition.
The idea underneath. Angle measures are additive — when an angle is decomposed into non-overlapping parts, the measures of the parts always add together to equal the measure of the whole angle.
2On level
Three angles meet to form a straight line, as shown below. Find the measure of the missing angle.
°
Show the answer and how to solve it
Answer. 55
The missing angle measures $55°$ . The three angles together form a straight line ( $180°$ ), and the two known angles ( $45° + 80° = 125°$ ) leave $55°$ for the missing angle.
1. 1The three angles meet at a point on a straight line, so their measures add up to $180°$ .
2. 2Add the two known angles together.
3. 3Subtract the sum from $180°$ to find the missing angle.
4. 4The missing angle measures $55°$ .
Common mistake. A common mistake is finding the sum of the known angles and stopping there, writing $125°$ instead of $55°$ . Another is using $90°$ as the whole instead of $180°$ — since $125°$ already exceeds $90°$ , this error produces an impossible negative result.
The idea underneath. When several angles share a vertex on a straight line, their measures add up to $180°$ . To find a missing angle, add the known angles and subtract that sum from $180°$ .
3On level
A student claims that parts 1 and 2 together make a valid split of angle AVB.
Select the statement that best describes the student's claim.
A
The student's claim is correct: the two parts exactly fill angle AVB.
B
The student's claim is incorrect because a part extends outside angle AVB.
C
The student's claim is incorrect because the parts leave a gap inside angle AVB.
D
The student's claim is incorrect because the parts overlap inside angle AVB.
Show the answer and how to solve it
The student's claim is incorrect: the two marked parts leave a gap between part 2 and ray VA. A valid split must fill the whole angle from boundary to boundary with no gaps, no overlaps, and no parts extending outside.
1. 1Look at angle AVB in the diagram. The boundary rays of the whole angle are ray VA and ray VB. The marked parts are part 1 and part 2.
2. 2A valid split must do all four things: cover the whole angle from one boundary ray to the other, leave no gaps between parts, have no overlapping parts, and have no parts extending outside.
3. 3Trace the parts in the diagram. Part 1 starts at ray VB and ends at the first interior ray. Part 2 starts there and ends at the second interior ray. But that second interior ray does NOT reach ray VA — there is empty space between part 2 and ray VA.
4. 4The two parts leave a gap between part 2 and ray VA. They do not fill angle AVB. The best description of the student's claim is that it is incorrect because the parts leave a gap inside angle AVB.
Common mistake. A common mistake is choosing overlap when there is actually a gap. Look carefully near ray VA — overlap means parts share space; gap means there is empty space.
The idea underneath. A valid split fills the whole angle exactly: from one boundary ray to the other, with no gaps, no overlaps, and no parts extending outside.
4Stretch
The diagram shows one whole angle split into two parts. The whole angle measures $85^{\circ}$ . Which equation matches the diagram?
A
$\displaystyle 27^{\circ} + {}$
$\displaystyle 58^{\circ} = {}$
$\displaystyle 85^{\circ}$
B
$\displaystyle 58^{\circ} + {}$
$\displaystyle 58^{\circ} = {}$
$\displaystyle 85^{\circ}$
C
$\displaystyle 27^{\circ} + {}$
$\displaystyle 85^{\circ} = {}$
$\displaystyle 58^{\circ}$
D
$\displaystyle 27^{\circ} + {}$
$\displaystyle 58^{\circ} = {}$
$\displaystyle 88^{\circ}$
Show the answer and how to solve it
The correct equation is $27^{\circ} + 58^{\circ} = 85^{\circ}$ . The two part measures $(27^{\circ}$ and $58^{\circ})$ add together to equal the whole angle measure $(85^{\circ})$ .
1. 1Look at the diagram. The two parts of the whole angle are labeled $27^{\circ}$ and $58^{\circ}$ . The whole angle measures $85^{\circ}$ .
2. 2When a whole angle is split into two parts, the two parts add together to equal the whole.
3. 3Substitute the values from the diagram:
4. 4Check the addition: $27 + 58 = 85$ . The equation $27^{\circ} + 58^{\circ} = 85^{\circ}$ matches the diagram.
Common mistake. A common mistake is using the whole angle $(85^{\circ})$ as one of the addends. Remember: the whole is the BIG angle made up of the two parts — it is what the parts ADD UP TO, not one of the parts itself.
The idea underneath. When a whole angle is split into smaller parts, the parts always add together to equal the whole. This is the additive property of angle measure.