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