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 7º more than the first. The third angle
is 7º less than ten times the first. Find the
measures of the angles.
The measure of the first angle is x = 17º.

Answer 1

9514 1404 393

Answer:

1. 15°
2. 22°
3. 143°

Explanation:

Let x represent the measure of the first angle. Then the second is x+7, and the third is 10x-7.

The sum of the three angles of the triangle is 180°, so we have ...

x +(x +7) +(10x -7) = 180

12x = 180 . . . . . . . . . . . . . . . collect terms

x = 15 . . . . . . . . . divide by 12 (first angle)

x +7 = 22 . . . . . .second angle

10x -7 = 150 -7 = 143 . . . . . third angle

The three angles are 15°, 22°, and 143°.