Answer:
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
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Add Equations (4) and 5).
2A = 190 Divide each side by 2
A = 95°
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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°
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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
