The measure of the largest angle of a triangle is 10° more than the sum of the measures of the other two angles and 10° less than 3 times the measure of the smallest angle. find the measures of the three angles of a triangle. (show all the work).

A = 95°; B = 50°; C = 35 °

Step-by-step explanation:

Let the three angles be A, B, and C, with A being the largest and C the smallest angle.

We have three conditions:

(1) A + B + C = 180

(2) A = B + C + 10

(3) A - 3C = -10

Let’s rearrange the equations to have the same form:

(4) A +  B  +  C  = 180

(5) A – B  –  C  =   10

(6) A        – 3C =  -10

Add Equations (4) and 5).

2A = 190     Divide each side by 2

 A = 95°

Substitute the value of A into Equation (6).

95 – 3C = -10       Subtract 95 from each side

      -3C = -105     Divide each side by -3

         C = 35°

Substitute the values for A and C into Equation (4).

95 + B + 35 = 180

      B + 130 = 180     Subtract 130 from each side

               B = 50°

A = 95°; B = 50°; C = 35 °

Check:

(1) 95 +50 + 35 = 180

                 180 = 180

(2)               95 = 50 + 35 + 10

                  95 = 95

(3) 95 – 3× 35 = -10

        95 – 105 = -10

                  -10 = -10

by definition, an arc subtended by a central angle of some given measure has the same measure. so .