Question

If the first angle of a triangle is x + 45, the second angle is (x + 45) - 30, and the third angle is 2x + (x + 45). What are the measurements of each angle? Remember the total of a triangle is 180.

Answer 1

Let's make it into an equation. (x + 45) + [(x + 45) -30] + [2x + (x + 45)] = 180

Now let's solve for x, first, lets remove the unnecessary parentheses (x + 45) + [x + 45 - 30] + [2x + (x + 45)] = 180, when we solve for it we get (x + 45) + [x + 15] + [2x + (x + 45)] = 180. We again remove unnecessary parentheses, (x + 45) + [x + 15] + [2x + x + 45] = 180 adding them up and getting (x + 45) + [x + 15] + [3x + 45] = 180. Now , lets remove the unnecessary parentheses which now is all of them x + 45 + x + 15 + 3x + 45 = 180. We add the like terms and the numbers getting us 5x + 105 = 180. We subtract 105 from both 105 and 180 getting us 5x = 75. We divide both sides by 5 getting x = 15. The first measurement, x + 45, will now be 15 + 45 making the first measurement 60. The second measurement, (x + 45) - 30, is now (15 + 45) - 30 making the second measurement 30. And finally the last measurement, 2x + (x + 45), is now 30 + (15 + 45) making the last measurement 90. You can verify this by adding it all up. 60 + 30 + 90 = 180.

Answer 2

first make an inequality to solve for x

(x + 45) + [(x + 45) - 30] + [2x + (x + 45)] = 180

x = 15


now plug x back into each equation and solve


first angle = 60°

second angle = 30°

third angle = 90°