The measure of the largest angle of a triangle is 90� more than the measure of the smallest
angle, and the measure of the remaining angle is 30� more than the measure of the smallest
angle. Find the measure of each angle. Show your work in obtaining your answer.
smallest = s
biggest = b
medium = m
b = s + 90
m = s + 30
s + m + b = 180
s + s + 30 + s + 90 = 180
3 s = 60 etc.....
To find the measure of each angle in the triangle, we can use the given information.
Let's assume the measure of the smallest angle is x.
According to the problem, the largest angle is 90 degrees more than the smallest angle, so its measure is (x + 90) degrees.
The remaining angle is 30 degrees more than the smallest angle, so its measure is (x + 30) degrees.
Remember that the sum of the angles in a triangle is always 180 degrees. So we can write an equation:
x + (x + 90) + (x + 30) = 180
Simplifying the equation:
3x + 120 = 180
Subtracting 120 from both sides:
3x = 60
Dividing both sides by 3:
x = 20
So, the measure of the smallest angle is 20 degrees.
Now we can find the measure of the other angles:
Largest angle = x + 90 = 20 + 90 = 110 degrees
Remaining angle = x + 30 = 20 + 30 = 50 degrees
Therefore, the measure of each angle in the triangle is 20 degrees, 110 degrees, and 50 degrees.