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Answers:

  • angle K = 50 degrees
  • angle L = 90 degrees
  • angle KML = 40 degrees
  • angle LMN = 140 degrees

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Explanation:

Rule: The interior (inside) angles of a triangle always add to 180

K+L+M = 180

5x+9x+4x = 180

18x = 180

x = 180/18 ... divide both sides by 18

x = 10

That x value directly leads to...

  • angle K = 5x = 5*10 = 50 degrees
  • angle L = 9x = 9*10 = 90 degrees (aka right angle)
  • angle M = 4x = 4*10 = 40 degrees

As a check,

K+L+M = 50+90+40 = 180

This confirms we have the right x value.

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We can further say,

  • angle KML = interior angle M = 40 degrees
  • angle LMN = 180 - (angle KML) = 180 - 40 = 140 degrees

note how interior angles K and L add to exterior angle LMN

50+90 = 140

This is an application of the remote interior angle theorem.

Answer:

Angle K = 50

Angle L = 90

Angle KML = 40

Angle LMN = 140

Step-by-step explanation:

Solve for x. We know that triangles' interior angles add up to 180.

So, we can set the values to equal to 180 and solve for x.

5x + 9x + 4x = 180

Simplify.

18x = 180

Now, divide by 18.

x = 10

Now, plug 10 in for each angle.

Angle K = (5 * 10) = 50

Angle L = (9 * 10) = 90

Angle KML = (4 * 10) = 40

For this last angle, we use the supplementary theorem that says "angles that are supplementary to each other add up to 180".

So, we do angle LMN + 40 = 180

Angle LMN = (180 - 40) = 140

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