Question

Find the angle and addition postulate and segment addition postulate

Answer 1

The angle and addition postulate involve using the analytical method of vector addition to find the resultant vector's magnitude and direction.

Step-by-step explanation:

The angle and addition postulate involve the analytical method of vector addition. To add vectors A and B using this method, follow these steps:

1. Identify the x- and y-axes that will be used in the problem.
2. Find the components of each vector along the chosen axes using the equations Ax = A cos θ and Ay = A sin θ.
3. Calculate the horizontal and vertical components for both vectors.
4. Combine the horizontal components and vertical components separately.
5. Find the magnitude and direction of the resultant vector using the Pythagorean theorem and trigonometric identities.

Answer 2

1. ∠LMN = 167°

2.
`x = -9`

3. ∠LMT = 96 + x = 96 - 1 = 95°

4.
`x= 1`

5.
`x = 7`

Step-by-step explanation:

1.

We have ∠TMN = 144° & ∠LMT = 23° and we need to find ∠LMN which is sum of angles TMN & LMT ∴ ∠LMN = ∠TMN + ∠LMT = 144° + 23° = 167°

2.

We have , ∠GHI = 173° , ∠GHQ= 29 + x , ∠QHI = 162
`173 = 29 + x + 162 + x` + x, in order to find x we see in question that ∠GHI is sum of angles ∠QHI & ∠GHQ i.e.

⇒
`173 = 162 + x + 29 + x`

⇒
`2x = -18`

⇒
`x = -9`

3.

We have, ∠TMN = x + 72 , ∠LMN = 166°, ∠LMT = 96 + x. Here we know that ∠LMN is sum of angles ∠TMN & ∠LMT i.e.

⇒
`166 = 96 + x + x +72`

⇒
`x = -1`

∴ ∠LMT = 96 + x = 96 - 1 = 95°

4.

To find length we have line PR = 7 + x & line Q = 8 ∴

`8 = 7 + x\\x = 1`

5.

We have ,

`2x - 4 + 2x - 7 = 17\\4x -11 = 17\\4x = 28 \\x= 7`