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 7^∘ more than the first. The third angle is 7^∘ less than four times the first. Find the measures of the angles. The measure of the first angle is x=∘. The measure of the second angle is x+7=∘. The measure of the third angle is 4x−7=∘

Answer 1

To find the measures of the angles, set up equations based on the given information and solve for x. Then, substitute x into the expressions for the second and third angles to find their measures.

Step-by-step explanation:

To find the measures of the angles in the triangular-shaped park, let's set up some equations based on the given information:

Let the first angle be x.

The second angle is 7 degrees more than the first, so it is x + 7.

The third angle is 7 degrees less than four times the first, so it is 4x - 7.

Since the sum of the angles in a triangle is 180 degrees, we can set up the equation:

x + (x + 7) + (4x - 7) = 180

Simplifying the equation:

6x = 180

x = 30

Therefore, the measures of the angles are:

First angle: 30 degrees

Second angle: 30 + 7 = 37 degrees

Third angle: 4(30) - 7 = 113 degrees

Learn more about Angles in Triangles