Answer: The measure of each angle is 105°, 50°, and 25°.
Step-by-step explanation: The first step in solving this is writing down what you know.
In the phrase it tells you that "one angle of a triangle measures 80 more than the smallest", so we can say that one angle = 80 + smallest angle.
This can be simplified more to x = 80 + y
x = One Angle
y = Smallest Angle
Then if we continue with the phrase it says "a third angle is twice the smallest", so we can say that a third angle = 2(Smallest Angle).
This can be simplified more to z = 2(y)
z = Third Angle
We also know that a triangles angles add up to 180°, so we know x + y + z = 180.
So, with these equations we can now solve for x, y, and z.
The easiest way would be to simply just plug in x and z straight into the 180 equation as follows.
x = 80 + y
z = 2(y)
180 = x + y + z
180 = (80 + y) + y + (2y)
180 = 80 + 4y
100 = 4y
y = 25
Then we can use y to solve for the other two equations.
z = 2(25) x = 80 + 25
z = 50 x = 105
After completing that you are left with the three angles of the triangle, 25, 50, and 105.