1. ∠LMN = 167°
2. [tex]x = -9[/tex]
3. ∠LMT = 96 + x = 96 - 1 = 95°
4. [tex]x= 1[/tex]
5. [tex]x = 7[/tex]
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[tex]173 = 29 + x + 162 + x[/tex] + x, in order to find x we see in question that ∠GHI is sum of angles ∠QHI & ∠GHQ i.e.
⇒[tex]173 = 162 + x + 29 + x[/tex]
⇒[tex]2x = -18[/tex]
⇒[tex]x = -9[/tex]
3.
We have, ∠TMN = x + 72 , ∠LMN = 166°, ∠LMT = 96 + x. Here we know that ∠LMN is sum of angles ∠TMN & ∠LMT i.e.
⇒[tex]166 = 96 + x + x +72[/tex]
⇒[tex]x = -1[/tex]
∴ ∠LMT = 96 + x = 96 - 1 = 95°
4.
To find length we have line PR = 7 + x & line Q = 8 ∴
[tex]8 = 7 + x\\x = 1[/tex]
5.
We have ,
[tex]2x - 4 + 2x - 7 = 17\\4x -11 = 17\\4x = 28 \\x= 7[/tex]
