In the figure below, find

Explanation

1. You know from the figure that ∠XYZ and ∠MYN are vertical angles; hence m(∠XYZ) = m(∠MYN) or 4y - 10^o = 2y + 20^o
   • Subtract 2y from both sides
     • 4y - 10^o -2y = 2y + 20^o -2y
   • Complete addition/subtraction of like terms.  So, in left hand-side (4y - 2y = 2y) and on right hand side (2y - 2y = 0)
     • 2y - 10^o = 20^o
   • Add 10 to both sides 
     • 2y - 10^o + 10^o = 20^o + 10^o
   • Add similar terms on left hand side (-10 + 10 = 0) and on right hand side (20 + 10 = 30)
     • 2y = 30^o
   • Divide both sides by 2
     • \(\frac{2y}{2}\) = \(\frac{30^o}{2} \)
   • y = 15^o
2. To get m(∠XYZ), simply substitute the value of y you got in step a in  angle equation (4y - 10^o)
   1. m(∠XYZ) = 4y - 10^o = 4 * 15^o - 10^o = 50^o
3. You see that m(∠XYZ) + m(∠MYX)  = m(∠MYZ) = 180^o.  Since we know the value of m(∠XYZ) from step b (50^o), then m(∠MYX) = 180^o - 50^o = 130^o