The side MN of ΔLMN is produced to X. If ∠LNX = 117° and ∠M = $\frac{1}{2}$ ∠L, then ∠L is :

78°

We have,

 ∠L = 2∠M 

∠LNX = 117° 

∠M = \(\frac{1}{2}\) ∠L

We know that,

∠LNX + ∠LNM = 180°     

= ∠ LNM = 180° - ∠LNX

= ∠ LNM = 180° - 117° 

= ∠ LNM = 63° 

In  ΔLMN;

We also know that,

∠L + ∠LNM + ∠M = 180° 

= ∠L + 63° + \(\frac{∠L }{2}\) = 180° 

= 2∠L + 126° + ∠L = 180° × 2

= 3∠L = 360° - 126° 

= 3∠L = 234° 

= ∠L  = 78°