The measure of one angle of a triangle is 40. The measures of the other two angles are in a ratio of 3:4. What are the measures of these two angles?
Let the measures of the other two angles be 3x and 4x.
Since the sum of all three angles in a triangle is 180 degrees, we have the equation 40 + 3x + 4x = 180.
Combining like terms, we get 7x + 40 = 180.
Subtracting 40 from both sides, we have 7x = 140.
Dividing both sides by 7, we get x = 20.
Therefore, the measures of the other two angles are 3x = 3(20) = 60 degrees and 4x = 4(20) = 80 degrees.
The measures of these two angles are 60 and 80 degrees.