## The second angle of a triangle is 20 degrees greater than the first angle. The third angle is twice the second. Find the three angles. (Note

Question

The second angle of a triangle is 20 degrees greater than the first angle. The third angle is twice the second. Find the three angles. (Note: in any triangles, angle measures add up to … how many degrees?)

0

1. A triangles angles add up to 180 degrees. Using this knowledge, we can write an equation evaluating the first angle as x.
x + x + 20 + 2(x + 20) = 180
distribute the 2
x + x + 20 + 2x + 40 = 180
combine like terms
4x + 60 = 180
isolate the variable: subtract 26 from both sides
4x = 120
isolate the variable: divide each side by 4
x = 30
We can now determine the other sides using this information:
Side 1: 30 degrees
to get side 2 we need to add 20 to side 1 getting:
Side 2: 50
For the last one, we must multiply side 2 by 2 getting:
Side 3: 100

condensed:
side 1: 30
side 2: 50
side 3: 100

We can check this by adding all of our answers and seeing if they equal 180:
30 + 50 + 100 =180

Hope this helps!