Question

In ∆LMN, MN is extended to O. If ∠MLN = 100 – x, ∠LMN = 2x and ∠LNO = 6x – 5, find the value of x

Answer 1

Exterior angle is equal to the sum of the opposite interior angles

∠LNO = ∠MLN + ∠LMN

6x – 5 = 100° – x + 2x

6x – 5 + x – 2x = 100°

6x + x – 2x = 100° + 5°

5x = 105°

x = `(105^circ)/5` = 21°

x = 21°