Answer:
40°, 60°, 80°
Step-by-step explanation:
You want the measures of the three angles of a triangle if the larger angles are 20° and 40° greater than the smallest.
Middle angle
The largest angle is 20° more than the middle angle, and the smallest is 20° less. Then the sum of the three angles is 3 times the middle angle, which must be 180°/3 = 60°.
The three angles are 40°, 60°, 80°.
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Additional comment
If you need equations, you can designate the angles a, b, c, smallest to largest. Then c=a+40, and b=a+20. The sum is ...
(a) +(a +20) +(a +40) = 3a +60 = 180
Dividing by 3 tells you ...
a +20 = 60 . . . . . matches the value of b
a = 60 -20 = 40
c = 40 +40 = 80
If we were to write the equations in terms of b, we would have ...
(b -20) +b +(b +20) = 180
3b = 180
b = 60
This version gives a 1-step equation to solve instead of a 2-step equation, easier to do mentally.
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