Find the angle and addition postulate and segment addition postulate

1. ∠LMN = 167°

2.

3.  ∠LMT  = 96 + x = 96 - 1 = 95°

4.

5.

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 + x, in order to find  x we see in question that ∠GHI is sum of angles ∠QHI & ∠GHQ i.e.

⇒

⇒

⇒

3.

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

⇒

⇒

∴ ∠LMT  = 96 + x = 96 - 1 = 95°

4.

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

5.

We have ,

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