Answer:
m∠XYZ = 162°
Step-by-step explanation:
We can see that ∠XYZ is an exterior angle while ∠W and ∠X are the opposite interior angles.
We know that the exterior angle of triangle is equal to the sum of opposite interior angles
Given
m∠XYZ = (15x-18)°
m∠W = (5x+2)°
m∠X = (8x+4)°
Mathematically it can be written as:
m∠X+m∠W = m∠XYZ
[tex]8x+4+5x+2 = 15x-18\\13x+6 = 15x-18\\13x-15x = -18-6\\-2x = -24\\\frac{-2x}{-2} = \frac{-24}{-2}\\x = 12[/tex]
Putting x=12 in m∠XYZ
[tex]15x-18\\=15(12)-18\\=180-18=162[/tex]
Hence,
m∠XYZ = 162°
