Well, well, well, we have ourselves a pair of supplementary angles! Let's call the measure of angle ABC "x" because I'm feeling generous today.
Now, according to your question, angle DEF is 20 degrees less than 3 times the measure of ABC. So, let's have some fun with math:
DEF = 3x - 20
Since ABC and DEF are supplementary, their sum should be 180 degrees. So let's put on our clown shoes and set up an equation:
ABC + DEF = 180
Now, substitute the value of DEF with 3x - 20:
x + (3x - 20) = 180
Now, let's solve this equation like a true juggling master. Combining like terms, we get:
4x - 20 = 180
Adding 20 to both sides:
4x = 200
Dividing both sides by 4:
x = 50
So, the measure of angle ABC, or x, is 50 degrees. Now, plug this value back into our equation for DEF:
DEF = 3(50) - 20
DEF = 150 - 20
DEF = 130
Therefore, angle ABC measures 50 degrees, and angle DEF measures 130 degrees. Ta da!