Find the Angles

Question

The residents of a downtown neighborhood designed a​ triangular-shaped park as part of a city beautification program. The park is bound by streets on all sides. The second angle of the triangle is

6 degrees° more than the first. The third angle is 6 degrees° less than eight times

the first. Find the measures of the angles.

Answer 1

We know that all the angles of a triangle sum to 180 degrees.

Angle 1 = is unknown, so lets label it "x"

Angle 2 = x+6

Angle 3 = 8x-6

So, Angle 1 + Angle 2 + Angle 3 = 180 ->Substitute Values

(x) + (x+6) + (8x-6) = 180 -> Combine like terms

10x = 180 -> Divide by 10

x = 18

Substitute the value of x back into the Angle measures

Angle 1 = 18

Angle 2 = 18 + 6 = 24

Angle 3 = 8(18) - 6 = 144-6 = 138

Check yourself by adding all the angles together

18+24+138 = 180!