x=10, y=12
m∡NOW = 68º, m∡NWO= 68º and m∡WNO =44º
1) Given that Δ NOW is an isosceles triangle, and NO≅NW we can state:
So, we can write NO≅NW
7x-2 = 5y+8 Subtracting 5y from both sides:
7x -5y =2+8
7x-5y= 10
As the sum of the interior angles is 180º, then we can write:
3x +14 +7x -2 +5y+8 =180º Combining like terms
10x +5y +20=180 Subtracting 20 from both sides
10x +5y = 160
2) Now we can set a Linear System and solve for x, y and find the angle's measurements, using the Addition/Elimination Method:
7x-5y= 10
10x +5y = 160
------------------------
17x = 170 Divide both sides by 17
x=10
Plugg x=10 into the first equation since it is the simplest between those two equations:
7(10) -5y = 10
70 -5y = 10
-5y = 10 -70
-5y = -60
5y = 60
y= 12
3) Hence, the answers are:
x=10, y=12
m∡NOW = 5y+8 ⇒5(12) +8 ⇒ 68º
m∡NOW = 68º
m∡NWO = 7x -2 ⇒ 7(10) -2 = 70 -2 =68º
m∡NWO= 68º
m∡WNO = 180-(68+68) = 44º Subtracting from 180º
