Question

Solve for x and then solve for y.

Answer 1

x = 40° ; y = 62°

Explanation:

The figure consists of 2 triangles. According to Angle sum property in a triangle , sum of measure of all the angles of a traingle is equal to 180° .

So ,

`(3x - 18) + (x + 7) + (x - 9) = 180`

`= > 5x - 20 = 180`

`= > 5x = 180 + 20 = 200`

`= > x = (200)/(5) = 40`

Now using the angle sum property in another triangle ,

`(x + 21) + (x + 17) + y = 180`

`= > y + (40 + 21) + (40 + 17) = 180`

`= > y + 61 + 57 = 180`

`= > y + 118 = 180`

`= > y = 180 - 118 = 62`

Answer 2

y = 62

Explanation:

Since we need to solve for x first, we'll solve the left triangle first. A triangle equals 180 degrees, so with in mind:

x + 7 + 3x - 18 + x - 9 = 180

add like terms

5x - 20 = 180

add 20 to both sides

5x = 200

divide by 5

x = 40

Now we have x, input it into the equations for the second triangles:

x + 21 + x + 17 + y = 180

40 + 21 + 40 + 17 + y = 180

add/simplify

118 + y = 180

subtract 118 from both sides

y = 62