The second angle of a triangle is three times as large as the first. The third angle is 20 degrees larger than the sum of the first two. What are the measures of the angles?
The sum of three angles is 180
A+ 3A + (20+4A)=180
solve for A first.
A = 20, B = 40, C = 120
To solve this problem, we need to set up an equation based on the information given. Let's assume that the first angle is x degrees.
According to the problem, the second angle is three times as large as the first. So, the second angle is 3x degrees.
The third angle is 20 degrees larger than the sum of the first two angles. The sum of the first two angles is x + 3x = 4x. Therefore, the third angle is (4x + 20) degrees.
The sum of the three angles in a triangle is always 180 degrees. So, we can set up an equation:
x + 3x + (4x + 20) = 180
Simplifying the equation:
8x + 20 = 180
Subtracting 20 from both sides:
8x = 160
Dividing both sides by 8:
x = 20
Now that we know that the first angle is 20 degrees, we can find the second angle:
Second angle = 3x = 3 * 20 = 60 degrees
And we can find the third angle:
Third angle = 4x + 20 = 4 * 20 + 20 = 100 degrees
So, the measures of the angles are 20 degrees, 60 degrees, and 100 degrees.