Tanya has a triangular garden bed in her back yard. the measure of the angle c is 20° less than three times the measure of angle a, and the measure of angle b is 15° less than the measure of angle a. find the measures of the three angles. start your work by defining the unknown quantities in terms of a variable. show all work and write a complete answer, including units.

Using "a" to represent the measure of angle a, along with the fact that the sum of angles in a triangle is 180°, the problem statement tells us

... (3a -20) + (a -15) + a = 180

... 5a - 35 = 180 . . . . . . . . . . . eliminate parentheses, collect terms

... a - 7 = 36 . . . . . . . . . . . . . . divide by the coefficient of "a"

... a = 43 . . . . . . . . . . . . . . . . . add 7

... b = a - 15 = 28 . . . . . . . . . . use the relationship of a and b

... c = 3a - 20 = 3·43 -20 = 109 . . . . . use the relationship of a and c

Check our work

... a + b + c = 43 + 28 + 109 = 180 . . . . the sum is 180, as it should be

The measures of the three angles, a, b, c, are 43°, 28°, and 109°, respectively.

the graph in the attached figure

step-by-step explanation:

we have

using a graphing tool

the graph in the attached figure

the roots are ( x-intercepts) x=-0.5,x=1,x=3

the y-intercept is the point (0,3)