the second angle of the a triangle is twice as large as the first angle. the measure of the third angle is 20 degrees less than the second. how large is each angle?
First angle = A
second angle = B
Third angle = 3
A + B + C = 180
B = 2A
C = B - 20
B/2 + B + (B-20) = 180
5/2 B = 200
B = (2/5)*200 = 80
You finish it.
40 degrees 60 degrees and 80 degrees
To find the measures of the angles in the triangle, let's assign a variable to the first angle and use that variable to determine the measures of the other angles.
Let's say the first angle is x degrees.
According to the problem, the second angle is twice as large as the first angle. Therefore, the second angle would be 2x degrees.
Now, it is given that the measure of the third angle is 20 degrees less than the second angle. So, the third angle would be 2x - 20 degrees.
Since the sum of the angles in a triangle is always 180 degrees, we can add up the measures of the three angles and set them equal to 180 degrees:
x + 2x + (2x - 20) = 180
Simplifying the equation, we have:
5x - 20 = 180
Adding 20 to both sides:
5x = 200
Dividing both sides by 5, we get:
x = 40
Therefore, the first angle measures 40 degrees, the second angle measures 2x = 2(40) = 80 degrees, and the third angle measures 2x - 20 = 2(40) - 20 = 60 degrees.
So, the measures of the angles in the triangle are 40 degrees, 80 degrees, and 60 degrees.