n triangle JKL, angle J is seven less than angle L, angle K is 21 less than twice angle L, what is the measure of angle K?

Answer 1

Hello,

First, let's assign some terms or variables to your problem:

<J = x - 7

<K = 2x - 21

<L = x

Second, we know the sum of interior angles in a triangle is 180 degrees, correct?

Therefore: The following equation represents our problem.

x - 7 + 2x - 21 + x = 180 <------this is the three expressions from above in equation form

4x - 28 = 180 <------this is the equation after combining like terms

4x = 208 <------added 28 to both sides of your equation

x = 52

Third, we now can substitute 52 in the values of x for the measures of interior angles. Therefore:

<J = 52 - 7 = 45

<J = 45 <-----the measure of angle J

<K = 2(52) -21

= 83

= 83

<K = 83 <-----the measure of angle K

<L = 52 <-----the measure of angle L

<J = 45

<K = 83

<L = 52

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Sum = 180

Yes, the solution checks out and is valid. I hope I provided you the assistance you needed and wish you a great end of the week. If you have further questions or feedback regarding this solution, please do so in the add the comment feature of the solution. If you are in need of one on one tutoring, please feel free to contact me or any tutor. Best!

Answer 2

In triangles all interior angles add to 180 degrees and given the info in the problem we know:

J + K + L = 180

J = L - 7

K = 2L - 21

We can re-write the expression, in terms of L, now we'll only have one unknown to solve for:

J + K + L = 180

(L - 7) + (2L - 21) + L = 180

4L -28 = 180

4L = 208

L = 52

If L = 52, then K = 2L -21 = 2*52 - 21 = 104 - 21 = 83.

Angle K is 83 degrees.