Angle Addition

Adjacent Angles

Share vertex and a side

Angle Addition Postulate

• Small angle + Small Angle = Big angle

• If you are missing a SMALL angle - subtract

• If you are missing the BIG angle - add

Multiple Select

If you are missing one of the SMALL angles, you should:

• Add

• Subtract

Multiple Select

If you are missing the BIG angle you should:

• Add

• Subtract

Multiple Choice

 Find m∠FED 

•  8°

•  127°°  

•  63°

Multiple Choice

 Find m∠RSM

•  85°

•  195°  

•  55°

Multiple Choice

 Find m∠VUZ

•  22°

•  322° 

•  172°

Problems with Variables

On problems with variables, we want to add the pieces of the angle together and set it equal to the whole angle.

part + part = whole

Example:

Step 1: Name Your Pieces

Here we have, angles ∠RQS, ∠SQT, and ∠RQT.

Step 2: Label Your Pieces
Part: ∠RQS=4x-20
Part: ∠SQT=3x+14 
Whole: ∠RQT=155

Step 3: Set Up
Using part + part = whole, we have ∠RQS+∠SQT=∠RQT

Example:

Step 4: Plug in and Solve

Part: ∠RQS=4x-20
Part: ∠SQT=3x+14 
Whole: ∠RQT=155

∠RQS+∠SQT=∠RQT

4x-20+3x+14=155
              7x-6=155
                  7x=161
                    x=23

Multiple Select

Which of the following in an equation to solve for x?

Pick all answer that apply.

• 2x + 94 = 72

• 2x+72 = 94

• 94 + 72 = 2x

• 72 + 2x = 94

Fill in the Blanks

what is the value of x?

x =

Multiple Choice

Write an equation to solve for angle ADB.

* Hint: solve for x first.

• 3x + 8 = 138

• 3x + 8 + 138 = 6x + 4

• 3x + 8 + 6x + 4 = 138

• 6x + 4 = 138

Multiple Choice

The value of x?

x =

• 14

• 50

• 88

• 138

Multiple Choice

If m∠RST = (12x -1)°, m∠RSU = (9x -15)°,

and m∠UST = 53°, find each measure.

• x = 13

  m∠RST = 155°

  m∠RSU = 102°

• x = 3

  m∠RST = 35°

  m∠RSU = 12°

• x = 22

  m∠RST = 263°

  m∠RSU = 183°

• x = 8

  m∠RST = 95°

  m∠RSU = 57°

Multiple Choice

Solve

• x = 5

• x = 11

• x = 33

• x = 55

Multiple Choice

Solve

• 50°

• 58°

• 115°

• 226°

Bisecting an angle means dividing it into two congruent angles.

​

Fill in the Blanks

An angle is bisected, forming two new angles. Each new angle has a measure of 15°. What was the measure of the original angle? (enter number only)

Fill in the Blanks

After bisecting an angle, Eric has two new angles, each with a measure of 19°. What was the measure of the original angle? (number only)

Fill in the Blanks

Given the segment BP bisects ∠CBD Find m∠2 if m∠2 = 7x + 5 and m∠1 = 9x − 5.

FIND m∠2=

degrees

Multiple Choice

The figure shows a triangle with one of its angle bisectors. Find x if m∠2 = 4x + 5 and m∠1 = 5x − 2.

• x = 7

• x = 3

• x = -7

• x = 1/3