it shows an image of a triangle.

Question

J =3x
K =(12x+1)
L= (16x-7)
are the angles

a. Write an equation that would help you solve for the missing angle measures. Combine Like Terms! Remember the Triangle Sum Theorem.

b. Solve the equation to find the value of x. Show/Explain all of your steps using inverse operations!

Answer 1

a. The Triangle Sum Theorem states that the sum of the angles in a triangle is always 180 degrees. So, we can write the equation:

J + K + L = 180

b. Let's substitute the expressions for J, K, and L into the equation:

3x + (12x + 1) + (16x - 7) = 180

Now, let's combine like terms:

3x + 12x + 1 + 16x - 7 = 180
31x - 6 = 180

Next, let's isolate the variable x by adding 6 to both sides of the equation:

31x - 6 + 6 = 180 + 6
31x = 186

Finally, let's solve for x by dividing both sides of the equation by 31:

31x/31 = 186/31
x = 6

So, the value of x is 6.

Answer 2

Using your value of x from the previous question, solve to find the measure of each angle.(3 points)

m∠J =

m∠K =

m∠L =

Answer 3

We can substitute the value of x (which is 6) into the expressions for each angle to find their measures:

m∠J = 3x
m∠J = 3(6)
m∠J = 18 degrees

m∠K = 12x + 1
m∠K = 12(6) + 1
m∠K = 72 + 1
m∠K = 73 degrees

m∠L = 16x - 7
m∠L = 16(6) - 7
m∠L = 96 - 7
m∠L = 89 degrees

Therefore, the measures of the angles are:

m∠J = 18 degrees
m∠K = 73 degrees
m∠L = 89 degrees