Answer:
x = 27
Step-by-step explanation:
From the picture attached,
m∠PLM + m∠PLK = 180° [Linear pair of angles are supplementary]
m∠PLM + 3x = 180°
m∠PLM = 180° - 3x
Similarly, m∠PML + m∠PMN = 180° [Linear pair of angles]
m∠PML + (2x + 72)° = 180°
m∠PML = 180° - (2x + 72)°
From triangle PLM.
m∠PLM + m∠PML + m∠LPM = 180° [Sum of interior angles of a triangle = 180°]
(180 - 3x) + 180 - (2x + 72) + x = 180
180 - 3x - 2x - 72 + x = 0
-4x + 108 = 0
x = [tex]\frac{108}{4}[/tex]
x = 27
