angle ABC and DEF are supplementary angles. the measure of DEF is 20 degrees less than 3 times the amount of ABC. what are ABC and DEF.
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!
To find the measures of angles ABC and DEF, let's follow these steps:
Step 1: Assign a variable
Let's assign a variable to one of the angles. Since we don't know the measure of angle ABC, we can let ABC = x.
Step 2: Use the given information to form an equation
We are told that angles ABC and DEF are supplementary, which means the sum of their measures is 180 degrees. So, we can write the equation:
ABC + DEF = 180
We are also told that the measure of DEF is 20 degrees less than 3 times the amount of ABC. In other words, DEF = 3ABC - 20.
Step 3: Solve the equation
Substitute the value of DEF into the first equation:
ABC + (3ABC - 20) = 180
Combining like terms:
4ABC - 20 = 180
Add 20 to both sides:
4ABC = 200
Divide both sides by 4:
ABC = 50
Step 4: Substitute the value of ABC back into the equation to find DEF:
DEF = 3(50) - 20
DEF = 150 - 20
DEF = 130
So, the measure of angle ABC is 50 degrees, and the measure of angle DEF is 130 degrees.