Segment and angle addition postulate worksheet

Both postulates say the same thing: the two parts add to the whole. Once it is written as an equation there is nothing geometric left to do.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.



Sigma Prep · sigmaprep.io/worksheets Name Segment and Angle Addition Date Period Find each value asked for. Find $x$ with segment addition Points $V$ , $H$ , and $R$ lie on $\overline{Y D}$ . Find $x$ . Points $G$ and $D$ lie on $\overline{L U}$ . Find $x$ . $C$ is the midpoint of $\overline{F E}$ . Find $x$ . The three pieces make up $L E$ . Find $x$ . Find $x$ with angle addition Ray $P D$ is inside $∠ H P W$ , and $m ∠ H P W = {(8 x + 34)}^{\circ}$ . Find $x$ . $∠ D N C$ is a straight angle, and ray $N H$ is inside it. Find $x$ . Ray $A G$ bisects $∠ K A P$ . Find $x$ . $m ∠ J V H$ is $18^{\circ}$ more than $m ∠ W V J$ , and $m ∠ W V H = 108^{\circ}$ . Find $x$ . Solve midpoint problems $E$ is the midpoint of $\overline{D F}$ , and $H$ is the midpoint of $\overline{D E}$ . $D H = 3 x - 21$ and $E F = 4 x - 10$ . Find $D F$ . $E$ is the midpoint of $\overline{D F}$ . Find $x$ . $E$ is the midpoint of $\overline{D F}$ , $D E = x - 9$ and $D F = 6 x - 86$ . Find $E F$ . $E$ is the midpoint of $\overline{D F}$ , and $R$ is the midpoint of $\overline{D E}$ . $D R = 4 x - 10$ and $E F = x + 57$ . Find $x$ . Find a length or angle measure $B$ is between $A$ and $C$ . $A B$ is $9$ more than 3 times $B C$ , and $A C = 77$ . Find $B C$ . Point $W$ is inside $∠ G J D$ . $m ∠ G J W$ is 4 times $m ∠ W J D$ , and $m ∠ G J W$ is $84^{\circ}$ more than $m ∠ W J D$ . Find $m ∠ G J D$ . Point $W$ is inside $∠ V P Z$ . $m ∠ V P W = {(2 x - 4)}^{\circ}$ , $m ∠ W P Z$ is $22^{\circ}$ more than $m ∠ V P W$ , and $m ∠ V P Z = {(5 x - 6)}^{\circ}$ . Find $m ∠ V P Z$ . $B$ and $C$ lie on $\overline{A D}$ in that order. $A B = 2 x + 10$ , $B C = 4 x + 6$ , $C D = 2 x - 5$ , $A D = 75$ . Find $B C$ . Find overlapping segment lengths Find $C F$ . Find $R G$ . Find $L F$ . Find $H Y$ . Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Segment and Angle Addition

Date Period

Find each value asked for.

Find $x$ with segment addition
Points $V$ , $H$ , and $R$ lie on $\overline{Y D}$ . Find $x$ .
Points $G$ and $D$ lie on $\overline{L U}$ . Find $x$ .
$C$ is the midpoint of $\overline{F E}$ . Find $x$ .
The three pieces make up $L E$ . Find $x$ .

Find $x$ with angle addition
Ray $P D$ is inside $∠ H P W$ , and $m ∠ H P W = {(8 x + 34)}^{\circ}$ . Find $x$ .
$∠ D N C$ is a straight angle, and ray $N H$ is inside it. Find $x$ .
Ray $A G$ bisects $∠ K A P$ . Find $x$ .
$m ∠ J V H$ is $18^{\circ}$ more than $m ∠ W V J$ , and $m ∠ W V H = 108^{\circ}$ . Find $x$ .

Solve midpoint problems
$E$ is the midpoint of $\overline{D F}$ , and $H$ is the midpoint of $\overline{D E}$ . $D H = 3 x - 21$ and $E F = 4 x - 10$ . Find $D F$ .
$E$ is the midpoint of $\overline{D F}$ . Find $x$ .
$E$ is the midpoint of $\overline{D F}$ , $D E = x - 9$ and $D F = 6 x - 86$ . Find $E F$ .
$E$ is the midpoint of $\overline{D F}$ , and $R$ is the midpoint of $\overline{D E}$ . $D R = 4 x - 10$ and $E F = x + 57$ . Find $x$ .

Find a length or angle measure
$B$ is between $A$ and $C$ . $A B$ is $9$ more than 3 times $B C$ , and $A C = 77$ . Find $B C$ .
Point $W$ is inside $∠ G J D$ . $m ∠ G J W$ is 4 times $m ∠ W J D$ , and $m ∠ G J W$ is $84^{\circ}$ more than $m ∠ W J D$ . Find $m ∠ G J D$ .
Point $W$ is inside $∠ V P Z$ . $m ∠ V P W = {(2 x - 4)}^{\circ}$ , $m ∠ W P Z$ is $22^{\circ}$ more than $m ∠ V P W$ , and $m ∠ V P Z = {(5 x - 6)}^{\circ}$ . Find $m ∠ V P Z$ .
$B$ and $C$ lie on $\overline{A D}$ in that order. $A B = 2 x + 10$ , $B C = 4 x + 6$ , $C D = 2 x - 5$ , $A D = 75$ . Find $B C$ .

Find overlapping segment lengths
Find $C F$ .
Find $R G$ .
Find $L F$ .
Find $H Y$ .



Sigma Prep · sigmaprep.io/worksheets Name Segment and Angle AdditionAnswer keyVersion 1 Date Period Find each value asked for. Find $x$ with segment addition Points $V$ , $H$ , and $R$ lie on $\overline{Y D}$ . Find $x$ . $5$ Points $G$ and $D$ lie on $\overline{L U}$ . Find $x$ . $6$ $C$ is the midpoint of $\overline{F E}$ . Find $x$ . $7$ The three pieces make up $L E$ . Find $x$ . $4$ Find $x$ with angle addition Ray $P D$ is inside $∠ H P W$ , and $m ∠ H P W = {(8 x + 34)}^{\circ}$ . Find $x$ . $12$ $∠ D N C$ is a straight angle, and ray $N H$ is inside it. Find $x$ . $16$ Ray $A G$ bisects $∠ K A P$ . Find $x$ . $2$ $m ∠ J V H$ is $18^{\circ}$ more than $m ∠ W V J$ , and $m ∠ W V H = 108^{\circ}$ . Find $x$ . $10$ Solve midpoint problems $E$ is the midpoint of $\overline{D F}$ , and $H$ is the midpoint of $\overline{D E}$ . $D H = 3 x - 21$ and $E F = 4 x - 10$ . Find $D F$ . $108$ $E$ is the midpoint of $\overline{D F}$ . Find $x$ . $15$ $E$ is the midpoint of $\overline{D F}$ , $D E = x - 9$ and $D F = 6 x - 86$ . Find $E F$ . $8$ $E$ is the midpoint of $\overline{D F}$ , and $R$ is the midpoint of $\overline{D E}$ . $D R = 4 x - 10$ and $E F = x + 57$ . Find $x$ . $11$ Find a length or angle measure $B$ is between $A$ and $C$ . $A B$ is $9$ more than 3 times $B C$ , and $A C = 77$ . Find $B C$ . $17$ Point $W$ is inside $∠ G J D$ . $m ∠ G J W$ is 4 times $m ∠ W J D$ , and $m ∠ G J W$ is $84^{\circ}$ more than $m ∠ W J D$ . Find $m ∠ G J D$ . $140^{\circ}$ Point $W$ is inside $∠ V P Z$ . $m ∠ V P W = {(2 x - 4)}^{\circ}$ , $m ∠ W P Z$ is $22^{\circ}$ more than $m ∠ V P W$ , and $m ∠ V P Z = {(5 x - 6)}^{\circ}$ . Find $m ∠ V P Z$ . $94^{\circ}$ $B$ and $C$ lie on $\overline{A D}$ in that order. $A B = 2 x + 10$ , $B C = 4 x + 6$ , $C D = 2 x - 5$ , $A D = 75$ . Find $B C$ . $38$ Find overlapping segment lengths Find $C F$ . $14$ Find $R G$ . $36$ Find $L F$ . $41$ Find $H Y$ . $22$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Segment and Angle AdditionAnswer keyVersion 1

Date Period

Find each value asked for.

Find $x$ with segment addition
Points $V$ , $H$ , and $R$ lie on $\overline{Y D}$ . Find $x$ . $5$
Points $G$ and $D$ lie on $\overline{L U}$ . Find $x$ . $6$
$C$ is the midpoint of $\overline{F E}$ . Find $x$ . $7$
The three pieces make up $L E$ . Find $x$ . $4$

Find $x$ with angle addition
Ray $P D$ is inside $∠ H P W$ , and $m ∠ H P W = {(8 x + 34)}^{\circ}$ . Find $x$ . $12$
$∠ D N C$ is a straight angle, and ray $N H$ is inside it. Find $x$ . $16$
Ray $A G$ bisects $∠ K A P$ . Find $x$ . $2$
$m ∠ J V H$ is $18^{\circ}$ more than $m ∠ W V J$ , and $m ∠ W V H = 108^{\circ}$ . Find $x$ . $10$

Solve midpoint problems
$E$ is the midpoint of $\overline{D F}$ , and $H$ is the midpoint of $\overline{D E}$ . $D H = 3 x - 21$ and $E F = 4 x - 10$ . Find $D F$ . $108$
$E$ is the midpoint of $\overline{D F}$ . Find $x$ . $15$
$E$ is the midpoint of $\overline{D F}$ , $D E = x - 9$ and $D F = 6 x - 86$ . Find $E F$ . $8$
$E$ is the midpoint of $\overline{D F}$ , and $R$ is the midpoint of $\overline{D E}$ . $D R = 4 x - 10$ and $E F = x + 57$ . Find $x$ . $11$

Find a length or angle measure
$B$ is between $A$ and $C$ . $A B$ is $9$ more than 3 times $B C$ , and $A C = 77$ . Find $B C$ . $17$
Point $W$ is inside $∠ G J D$ . $m ∠ G J W$ is 4 times $m ∠ W J D$ , and $m ∠ G J W$ is $84^{\circ}$ more than $m ∠ W J D$ . Find $m ∠ G J D$ . $140^{\circ}$
Point $W$ is inside $∠ V P Z$ . $m ∠ V P W = {(2 x - 4)}^{\circ}$ , $m ∠ W P Z$ is $22^{\circ}$ more than $m ∠ V P W$ , and $m ∠ V P Z = {(5 x - 6)}^{\circ}$ . Find $m ∠ V P Z$ . $94^{\circ}$
$B$ and $C$ lie on $\overline{A D}$ in that order. $A B = 2 x + 10$ , $B C = 4 x + 6$ , $C D = 2 x - 5$ , $A D = 75$ . Find $B C$ . $38$

Find overlapping segment lengths
Find $C F$ . $14$
Find $R G$ . $36$
Find $L F$ . $41$
Find $H Y$ . $22$

How to do these

B is between A and C. $A B = 2 x + 3$ , $B C = 3 x - 1$ , $A C = 27$ . Find $x$

The parts add to the whole.
2x + 3 plus 3x - 1 equals 27.
5x + 2 = 27.

The answer is $5$ .

Where students go wrong

Setting the two parts equal to each other rather than to the whole. They are only equal if the point happens to be the midpoint, which these questions do not say.

Also called segment and angle addition postulates or adding segments and angles.

What you can put on this worksheet

The segment addition postulate: Find $x$ . — points a, b, c on a line, labeled A, B, C, 31, 8, 2x + 27 → $6$
The angle addition postulate: Ray $R K$ is inside $∠ T R M$ , and $m ∠ T R M = {(5 x + 25)}^{\circ}$ . Find $x$ . — angle trm with ray rk inside it, labeled T, K, M, R, 37°, 23° → $7$
Midpoints, written in x: $B$ is the midpoint of $\overline{A C}$ . Find $x$ . — points a, b, c on a line, labeled A, B, C, 62 → $8$
Find the length or angle, not just x: Point $L$ is inside $∠ T B N$ . $m ∠ T B L$ is $11^{\circ}$ more than $m ∠ L B N$ , and $m ∠ T B N = 149^{\circ}$ . Find $m ∠ T B L$ . — angle tbn with ray bl inside it, labeled T, L, N, B → $80^{\circ}$
Overlapping lengths: Find $N B$ . — points n, z, b, p on a line, labeled N, Z, B, P, 7, x + 8, x + 14, 31 → $22$

Questions about these worksheets

Yes. Every segment and angle addition postulate sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Geometry is usually taken around 9th or 10th grade, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the segment and angle addition postulate questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

You pick from 5: the segment addition postulate, the angle addition postulate, midpoints, written in x, find the length or angle, not just x and overlapping lengths. Tick as many as you want and set how many of each, or let it spread them evenly.

Setting the two parts equal to each other rather than to the whole. They are only equal if the point happens to be the midpoint, which these questions do not say.

Segment and angle addition postulate worksheet

Select your difficulty

Find xxx with segment addition

Find xxx with angle addition

Solve midpoint problems

Find a length or angle measure

Find overlapping segment lengths

Find xxx with segment addition

Find xxx with angle addition

Solve midpoint problems

Find a length or angle measure

Find overlapping segment lengths

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these segment and angle addition postulate worksheets free?+

Do the segment and angle addition postulate worksheets come with an answer key?+

Are these segment and angle addition postulate worksheets printable?+

What grade are these segment and angle addition postulate worksheets for?+

Can I get a different version of the same segment and angle addition postulate worksheet?+

Is this a free alternative to Kuta Software for segment and angle addition postulate?+

Can I choose how hard the segment and angle addition postulate questions are?+

What kinds of question are on a segment and angle addition postulate worksheet?+

What do students get wrong with segment and angle addition postulate?+

Find $x$ with segment addition

Find $x$ with angle addition

Find $x$ with segment addition

Find $x$ with angle addition