Question 844980: the measure of the largest angle of a triangle is 90 degrees more than the measure of the smallest angle, and the measure of the remaining angle is 30 degrees more than the measure of the smallest angle, find the measure of each angle.
Answer by pmesler(52)   (Show Source):
You can put this solution on YOUR website! The easiest way to tackle this problem is to know that in Geometry, there is a rule that states that the sum of all the angles in a triangle will always add up to 180 degrees.
Let x = the smallest angle.
Let x + 30 = the angle that is 30 degrees more than the smallest angle.
Let x + 90 = the angle that is 90 degrees more than the smallest angle.
Therefore, given the rule above we can solve for x by writing,
x + (x+90) + (x+30) = 180
Combine like terms:
3x + 120 = 180
Subtract each side by 120.
3x = 60
Divide each side by 3.
x = 20
Therefore the smallest angle is 20 degrees, the second largest angle is 20 + 30 = 50 degrees, and the largest angle equals 20 + 90 = 110 degrees. To check if this is correct, add all the angles to see if it equals 180 degrees:
20 + 50 + 110 = 180 degrees. It checks out so the answer is correct.
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