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Sagot :

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

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